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Let f be the function with f(0) = 1/ (pi)^2, f(2) = 1/(pi)^2, and the derivative given by f'(x) = (x+1)cos ((pi)(x)). How many values of x in the open interval (0, 2) satisfy the conclusion of the Mean Value

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  1. Calculus

    f(x) = x2 + 2x - 1 Compute the derivative (that is, the derivative function) by evaluating the limit. Show your work. (Notice that for the function k(x), you’ll have to compute the limit differently depending on whether x < 2 or x > 2, and you’ll end
  2. Calculus

    Og Function: -cos(3x) Derivative Function: 3 sin(3x) The period for the function and its derivative is 2π/3 radians. Over one period, when is the derivative function equal to its original function? That is, when is f(x) = f '(x) over 0≤x≤2π/3? Round
  3. Calculus

    Use a symbolic differentiation utility to find the derivative of the function g(x)=x�ã((x^2)+1). Use the utility to graph the function and is derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any
  4. Calculus

    What would an example of a logarithmic function that contains two trig functions within it where you would need to use chain rule and product rule to take derivative look like? How would taking the derivative of the function in its original form look
  5. Calculus HELP

    Original Function: -cos(3x) Derivative Function: 3 sin(3x) The period for the function and its derivative is 2π/3 radians. Over one period, when is the derivative function equal to its original function? That is, when is f(x) = f '(x) over 0≤x≤2π/3?
  6. CAL

    The _____________ of a function is a formula for the slope of the tangent line to that function at any point x. When the function is defined as f(x), the derivative will be written as __________or ________. When the function is written in the form of y =,
  7. math

    I have the same project as Jill down there... -What is the definition of a derivative? -What does the derivative of a function tell you (in english) ? Then I need an example of the power rule, quotient rule, and chain rule. -What information does the FIRST
  8. Calculus

    What would an example of a logarithmic function that contains a radical within it and a quotient within it where you would need to use chain rule and quotient rule to take derivative look like? How would taking the derivative of the function in its
  9. Calc

    I'm creating a "calculu for dummies" project book. I've already done most of it, I'm just stuck on these ones. Thank you! -What is the definition of a derivative? -What does the derivative of a function tell you (in english) ? Then I need an example of the
  10. calculus

    If you have the derivative of a function, you normally can take the antiderivative in order to find almost the exact original function (say almost since any number that doesn’t have a variable would just have C replace it since we can’t calculate that
  11. math

    Let f be a real value function and x Î Df then 0 lim ( ) ( ) h f x h f x ® h + - when it exists is called A) The derivative of f at a B) The derivative of f at h C) The derivative of f at x D) The derivative of f at x = h
  12. CALC 1

    Suppose that h is a function with h'(x) = xe^x. Find all intervals where the function h is concave up. Now, I understand that concavity is determined by the second derivative, so what my question here is, is it just taking the first derivative and then
  13. calculus

    Find the derivative of the function using the definition of derivative. g(t)= 9/sqrt(t) g'(t)= state the domain of the function and the domain of the derivative (use interval notation)
  14. Calc. checking answer

    Determine whether or not each of the following functions is invertible. Give your reasons for believing the function is invertible or not. Please check this for me. I am not sure if I am adequately explaining my answer and if my answer is right. a) y=
  15. Calc

    a) y =ln(x-1) find dy/dx=? b) y=3 ln x - ln (1/x) where x >0, dy/dx= ? My teacher says the answers are a) (2x)/(x^2-1) and b) 4/x I am not sure how you find the derivative when they involve ln. Could you please explain to me how to get these answers? I
  16. Calculus

    Hello I need help with this excersise of derivative of a inverse function. The excersise says: If f(x+2)=x^3+1 and g(x)=f(arctg x), find the derivative of the inverse function of g(x) and then calculate (g^-1 (9))'[the derivative of the inverse function
  17. Applied Calculus

    Find the first and second derivative of the function: x/(7x+10) Using quotient rule. This is part of my homework in the section named "Higher Order Derivatives". I am confused on getting the second derivative, as I found the first derivative to be
  18. Math - derivative of sinusoidal (check)

    a) Find a function y=f(x) that satisfies the differential equation dy/dx = fifth derivative. This is one of the questions in my practice test, I tried the basic equation of the trig function such as f(x)= sin(x) or f(x)=-sin(x) however in the fourth
  19. CALCULUS HELP

    Find the second derivative for the function 5x^3+60x^2-36x-41 and solve the equation F(X)=0 i got to the second derivative but what do we do next to be able to get one of these answers.. F(x) = 5x3+60x2−36x−41 1. derivative of F(x) with respect to x =
  20. increasing and decreasing intervals

    Have to find the intervals on which f(x) = 4 - sqrt(x+2) is increasing. Also the intervals on which the function is decreasing. TIA Find the derivative of f(x). When the derivative is positive, the function increases as x increases. When the derivative is
  21. inverse

    If f(x)=cosx + 3 how do I find f inverse(1)? Thanks y = cos(x) + 3 the inverse of this is x = cos(y) + 3 solve for y and you have your inverse The cos function only has a range of [-1,1], so the range of f(x) is [2,4]. this means f inverse of 1 doesn't
  22. increasing decreasing and more

    How to analytically find the intervals on which the function y = 2x^4 - 4x^2 + 1 is 1)increasing 2)decreasing 3)concave up 4)concave down Also find any local extreme values and inflection points. Thanks. (1) The function is increasing when the first
  23. Calculus (Continuity and Differentiability)

    Okay. So I am given a graph of a derivative. From what I can gather, it looks like the function might be abs(x-2)-4. (I was not given an explicit function for g', just its graph.) The question then goes on to ask me: Is it possible, impossible, or certain
  24. calculus

    please help! having issue with exponent part of problem. I come to 16x^4 but I think it should be 16x^3.i also have complications with finding the domains. find the derivative of the function using the definition of derivative. f(x)=4x^4 f'(x)=? State the
  25. Calculus

    Find the intervals on which y=1/(x^2+1)^2 is increasing and decreasing. find the first derivative which is -4x/(x^2+1)^3 you should know that if the first derivative is positive, then the function is increasing and if it is negative, the function is
  26. Quantum mechanics, eigenfunctions!

    Determine if the function sin(x)*e^(ax) where a=constant is an eigenfunction of the operators d/dx and d^2/(dx)^2 Okay. My understanding is that you use the operator and perform its "thing" on the function. In this case, you will have to find the 1st
  27. calculus

    You are given the following function. f(x)= (8+x)/(1-8x) (a) Find the derivative of the function using the definition of derivative. (b) Give the domain of the function. c) Give the domain of derivative of function?
  28. calculus

    Suppose you know that f(u) is a function with derivative f’(u). Then the derivative with respect to t, of the composite function f(ln(kt)) is what? A. f’(1/(kt)) B. (f’(ln(kt)))/t C. f’(1/t) D. (f’(ln(kt)))/kt E. None
  29. Calc-please help!

    What is the second derivative of (x^3)/(x^2-1)? And how would I accurately graph both the derivative and the second derivative of this function?
  30. Calculus

    71st derivative of the function 𝑓(𝑥) = sin^4 x − cos^4 x when x =(𝜋)/2, So, your challenge is to look for patterns to determine the 71st derivative of the above function evaluated at x =(𝜋)/2.
  31. math

    can some one please help me with the following questions as i don't understand them please (a) write down the derivative of each of the functions f(x)=E7x and g(x)=cos(2x) using the product rule differentiate the function k(x)=E7xcos(2x) (b)write down the
  32. Calculus

    Determine whether or not each of the following functions is invertible. Give your reasons for believing the function is invertible or not. Please check this for me. I am not sure if I am adequately explaining my answer and if my answer is right. a) y=
  33. Calculus

    How many critical points does the function f(x) = [(x-2)^5][(x+3)^4] have? A. 1 B. 2 C. 3 D. 5 E. 9 --- Ok, these are my thoughts on this question: My impulse was to do derivative of the function. However, if I'm going to set the function equal to zero to
  34. Calculus

    For f(x)=2(x+5)^3 +7 Find and classify the extreme values, determine where the function is increasing and decreasing, where it is concave up and concave down, and any points of inflection. I understand this is using the first and second derivative tests,
  35. Calculus--> bobpursley

    How do you get m=0? from taking the second derivative? does c=1? Can you check my work on how I get the derivative of R=M^2(c/2-m/3) NEXT R=1/2(CM^2)-1/3(M^3) NEXT dR/dM=CM-M^2. I checked in the back, and that was the answer for the first part of the
  36. Calc 121

    Okay, how would you go about finding the area of a curve from 1 to 4, when y=2x+(2/(x^2))?? It's not like the problem I asked before because here, you cannot use substitution. I tried using 2x for u and x^2 for du but it won't simplify into a ln problem or
  37. Calculus HELP ASAP

    Listed below are four types of functions. Which does not possess a derivative of the same type? a) exponential function b) logarithmic function c) sinusoidal function d) linear function e) NO RESPONSE
  38. Calculus

    Find the derivative of the function using the definition of a derivative. F(x)=squareroot(1-3x) Please show work for understanding, thank you! :)
  39. Calculus

    f(x) = x2 + 2x - 1 Compute the derivative (that is, the derivative function) by evaluating the limit. Show your work.
  40. Calculus

    g(x) = -500/x , x does not equal 0 Compute the derivative (that is, the derivative function) by evaluating the limit
  41. Calculus

    Use derivative formulas to find the derivative of the function. please show your work h(x)=10^3-25x^6+3x^15
  42. Numerical Analysis

    Use forward and backward difference approximations of O(h) and a centered difference approximation of O(h 2 ) to estimate the first derivative of the function below. Evaluate the derivative at x = 2 using a step size of h = 0.2. Compare your results with
  43. Calculus

    Suppose you know f(u) has the derivative f'(u). find the derivative with respect to t of the composite function f(ln(kt)+t^2)
  44. Calculus review

    let the function h(x)= (integrand symbol from 2 to x^2)arctan (t) dt. Find h'(x). This question confused me because i know the derivative of an integral is the original function. I just need help with finding the derivative of that integral. I don't know
  45. Calculus

    k(x) = |x - 2| Compute the derivative (that is, the derivative function) by evaluating the limit
  46. Calculus HELP

    Determine the derivative of the function ƒ(x) = x^3 − 12x^2. Now determine the derivative of the function g(x) = x^3 − 12x^2 + 6. How are the two functions related? How are the derivatives of the two functions related? I know the derivative, however
  47. Calculus

    Explain the global optimization process for a continuous function over a closed interval. Be sure to identify all steps involved and clearly explain how the derivative is utilized in this process. Does this have to do with the first derivative rule or
  48. Calculus

    Explain the global optimization process for a continuous function over a closed interval. Be sure to identify all steps involved and clearly explain how the derivative is utilized in this process. Does this have to do with the first derivative rule or
  49. Calculus (Global Max)

    Explain the global optimization process for a continuous function over a closed interval. Be sure to identify all steps involved and clearly explain how the derivative is utilized in this process. Does this have to do with the first derivative rule or
  50. Calculus-Function

    sketch the graph of a function in neighborhood x=2 that satisfies these conditions f(2)=3 f'(2)=2 f"(2)=-1 you can find a specific function that satisfies all of the given conditions i know the first derivative gives you critical points, and second
  51. math

    Find the derivative function for the following functions using the first principles definition of the derivative limh→0f(x+h)−f(x)h . Show all your steps and include proper notation. a. (4) ƒ(x) = 5x3 b. (5) ƒ(x) = 12x c. (6) ƒ(x) = √2x
  52. math

    Hi, I am in need of some help. How would I find the derivative of the function: f(x) = int e^sin(t) dt if the upper bound is x^2 and the lower bound is cos(x)? I'm not really sure what to do here since e^sin(t) is not an integratable function. Should I
  53. Calculus

    Suppose that you can calculate the derivative of a function using the formula f(x) = 2f(x) + 4x. If the output value of the function at x=4 is 3 estimate the value of the function at 4.012. Linear Approximation right? I'm not seeing an f'(x) anywhere. Can
  54. Calculus

    If I have a function f(x), and am given its derivative, f'(x): may I take it as a given that f(x) is an integral of f'(x). My reasoning is that 'undoing' the derivative gives me the derivative. Eg is 1/3x^3 an integral of x^2? Thanks.
  55. Calculus derivatives

    f(a) = a + √a (a) Find the derivative of the function using the definition of derivative.
  56. calculus

    Calculate the derivative of the function. Then find the value of the derivative as specified. f(x) = 8/(x+2); f '(0)
  57. calculus

    Use the function defined below to calculate the indicated derivative. f(t)= 4/(t^3)+3 what is f''(2) (second derivative) Need help!!
  58. Calculus

    I finished this problem but I wanted some feedback because I don't know if it's entirely correct. Suppose that functions f and g and their derivatives with respect to x have the following values at x=2. f(x)=8 g(x)=2 f'(x)=1/3 g'(x)=-3 Find d/dx of f(g(x))
  59. Calculus. I need help!

    Write the composite function in the form f(g(x)). [Identify the inner function u=g(x) and the outer function y=f(u).] Then find the derivative dy/dx. y=√sinx √ is square root.
  60. calculus

    Suppose that you can calculate the derivative of a function using the formula f′(x)=2f(x)+4x. If the output value of the function at x=4 is 4 estimate the value of the function at 4.006.
  61. calculus 2

    Suppose that you can calculate the derivative of a function using the formula f'(x) = 4f(x) + 2x. If the output value of the function at x= 4 is 2 estimate the value of the function at 4.013
  62. Calculus c

    Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis at x=-1 and x=3 and has a
  63. math

    Given the function g (x) = 6x^3 + 54x^2 + 90x , find the first derivative, g'(x) . Now, we want to know whether there is a local minimum or local maximum at x = − 1 , so we will use the second derivative test. Find the second derivative, g ' ' ( x ) . g
  64. calc

    i did this problem and it isn't working out, so i think i'm either making a dumb mistake or misunderstanding what it's asking. A particle moves along the x axis so that its velocity at any time t greater than or equal to 0 is given by v(t) = 1 -
  65. Please check my Calculus

    1. Find all points of inflection of the function f(x)=x^4-6x^3 A. (0, 0) B. (0, 0), (9/2, -2187/16) C. (3, -81) D. (0, 0), 3, -81) E. none of these I got D. I found the second derivative and solved for x and plugged values into original function to get
  66. Calculus

    Consider a differentiable function f having domain all positive real numbers, and for which it is known that f'(x)=(4-x)x^-3 for x>0. A. Find the x-coordinate of the critical point of f. Determine whether the point is a relative maximum, a relative
  67. Calculus

    Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis at x=-1 and x=3 and has a
  68. Calculus

    R=M^2(c/2-m/3) dR/dM=CM-M^2 I found the derivative. Now how would I find the vale of M that maximize the derivative dR/dM? set it to zero, and solve for m. You get two solutions. Use the second derivative to see which one is the max. I get M=C. How do I go
  69. Calculus (Derivatives)

    What is the derivative of the this functon? g(x) = -500/x, x cannot equal 0. I know that in order to fnd the derivative I need to put the function into the equation for evaluating derivatives as limits. lim as h -> 0 (f(x+h) - f(x))/h I did this, but I am
  70. math

    i need to find when the function increases or decreases, this is the derivative of the function (10 − 3x)/(2 ¡î5 − x) but how do you solve the function when x is zero?
  71. calc

    derivative of (x^3/6)+(1/2x)? i got (x^2/2)-(1/2x^2) is that correct? and then wut is the (F'(x))2?...meaning the derivative squred? if you meant (1/2)x^2 - 1/(2x^2) you are correct I don't think they are looking for the square of the derivative, but
  72. math

    Given the function g (x) = 6x^3 + 72x^2 + 270x , find the first derivative, g'( x) . g'( x ) = Notice that g ' ( x ) = 0 when x = − 5 , that is, g ' ( − 5 ) = 0 . Now, we want to know whether there is a local minimum or local maximum at x = − 5 , so
  73. Calc, Mean Value Theorem

    Consider the function : 3x^3 - 2x^2 - 4x + 1 Find the average slope of this function on the interval. By the Mean Value Theorem, we know there exists a "c" in the open interval (-2,3) such that f'(c) is equal to this mean slope. Find the two values of "c"
  74. calculus

    1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))? 2. Find the derivative of f(x) = |x + 2| at the point (1, 3) 3. Find f '(x) for f(x) = -2x3 + 3x2 - x + 15. 4. Find all values of x on the
  75. Math

    find the derivative of x^3-6x^2+15x+8 and show by completing the square that function has no turning point. I can find derivative but not sure of next step
  76. Calculus

    1. is the derivative of the function f(x)=5e^(4x-9z) f'(x)= -25e^(4x-9z)? 2. Is the derivative of the function f(x)=e^(2x)-e^(-2x) f'(x)=2e^(2x)+2e^(-2x)? 3. If f(x)=e^-x^-1, would f'(2)=-1/4e^(1/4)?
  77. Calculus

    find the derivative of y= x^3+8/x+2 the / is meant to be a fraction bar, I am really really bad at finding the derivative of a fraction function, could you help by showing me exactly how, Thanks
  78. calculus

    For a function f(x) the derivative at x=2 is 5. Is the derivative of f(x) continuous at x=2? Thanks!
  79. calc

    d/dx integral from o to x of function cos(2*pi*x) du is first i do the integral and i find the derivative right. by the fundamental theorem of calculus, if there is an integral from o to x, don't i just plug the x in the function. the integral of the
  80. Applied calculas

    1. Consider the function y = xx (for x > 0). a) Why does the derivative rule for xn not apply? b) Why does the derivative rule for ax not apply? c) What are the four magic properties of logarithms? d) Take the ln of both sides. Use the properties of
  81. applied calculus

    1. Consider the function y = xx (for x> 0). a) Why does the derivative rule for xn not apply? b) Why does the derivative rule for ax not apply? c) What are the four magic properties of logarithms? d) Take the ln of both sides. Use the properties of
  82. Calc AB

    Remember that f(x) must be one-to-one (only one y-value for each x-value) over the domain where f –1(x)is defined as a function. So, in some cases you must restrict the domain of f(x) so that it's one-to-one. There might be more than one section of
  83. Math, Calculus

    Find the derivative of the function. y= xcosx - sinx What's the derivative? I get only one trig function. I will be happy to critique your work or thinking. Use the chain rule on the first term. Our class hasn't covered Chain Rule. Only product and
  84. Differentiation

    Again, that all makes sense. Thank you very much. Thank you very much. I did get the derivative you show, but then divided through by 6 to get at the stationary points. Was that wrong? I'm only looking for a critique please, not answers! given: f(x)= −2x
  85. Calculus (Help)

    Also I would like to know how to set this problem up in finding the answer: Find the second derivative. y= sqrt(3x+4) Thanks, P.S. I tried taking 3x+4 and squaring it to the 1/2. I thought that might've been the same, then I took the derivative of that and
  86. Calculus

    Decide if the following function f(x) is differentiable at x=0. Try zooming in on a graphing calculator, or calculating the derivative f'(0) from the definition. f(x) = x^4sin(2/x), if x is not equal to 0, and f(x) = 0 if x = 0. If it is differentiable,
  87. calculus

    1.) values of f(t) are given in the following table: t 0 2 4 6 8 10 f(t) 137 112 88 68 49 34 a. Does this function appear to have a positive or negative first derivative? Second derivative? * I think both derivatives are negative b. Estimate (f prime) f^'
  88. Calc

    1. Differentiae each function a) Y=-3x^2+5x-4 b) F(x) = 6/x-3/x^2 c) F(x)=(3x^2-4x)(x^3+1) 2. Determine the equation of the tangent line to the curve y=2x^2-1 at the point where x=-2 3. Evaluate, rounding to two decimal places, If necessary a) In 5 b) b)
  89. calculus

    is the function f(x)=x^2 increasing on decreasing at x = -1. can anyone please check my reasoning: the value of the derivative of the function at x=-1 is -2, so that means the slope of the tangent line to the graph at that is a negative value so the
  90. calculus

    Could someone check my reasoning? thanx Find the derivative of the function. sin(sin[sinx]) I need to use the chain rule to solve. So I take the derivative sin(sin[sinx) first. Then multiply that by the inside which is the derivative of sin[sinx]. And
  91. Precalculus

    Johnny's Tumblers sells plastic cups in bulk for start-up restaurants. Their cost for producing these is modeled by: c(x) = 0.02x^2 + 0.5x + 40 a) Since the marginal cost is found by taking the derivative, the formula for c'(x)= ? (My answer: 0.04x + 0.5)
  92. Math

    how do i minimize this function. 21L + (2600/L) Set the derivative equal to zero and solve for L. 21 - 2600/L^2 = 0 2600 = 21 L^2 There will be positive and negative solutions for L. You can use the second derivative test or direct calculation to see which
  93. math

    Consider the function defined below. y = 2t3 - 4t2 + 3 (a) Calculate the second derivative. y '' = (b) Calculate the third derivative. y ''' =
  94. calculus

    Find the first and second derivative - simplify your answer. y=x/4x+1 I solved the first derivative and got 1/(4x+1)^2 Not sure if I did the first derivative right and not sure how to do the second derivative.
  95. Calculus

    Alright, I want to see if I understand the language of these two problems and their solutions. It asks: If F(x) = [given integrand], find the derivative F'(x). So is F(x) just our function, and F'(x) our antiderivative? 1) F(x) = ∫(2, x)
  96. Calculus prince@18

    let the function h(x)= (integrand symbol from 2 to x^2)arctan (t) dt. Find h'(x). This question confused me because i know the derivative of an integral is the original function. I just need help with finding the derivative of that integral. I don't know
  97. Calculus

    Suppose that f is a differentiable function with derivative 𝑓'(𝑥) = (𝑥 − 3)(𝑥 + 1)(𝑥 + 5). Determine the intervals of x for which the function of f is increasing and decreasing.
  98. Calculus

    Consider the function y = 3x5 – 25x3 + 60x + 1. Use the first derivative test to decide whether this function has a maximum at x = 1
  99. Calculus(easy)

    Suppose the derivative of a function f is f′(x)=(x−5)^3(x−3)^4(x+18)^8. Then the function f is increasing on the interval Can anyone please help me with this problem. It seems simple, but I just do not understand it.
  100. Calc

    g'(x)=tan(2/1+x^2) Let g be the function with first derivative given above and g(1)=5. If f is the function defined by f(x)=ln(g(x)), what is the value of f'(1)? I know the answer is 0.311, but I need steps as to why. Please and thanks.

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