If g is a differentiable function such that g(x) is less than 0 for all real numbers x and if f prime of x equals (x2-4)*g(x), which of the following is true? A. f has a relative maximum at x=-2

22,638 results
  1. Pre-Calculus

    A rectangle is bounded by the x-axis and the semicircle y = √36 – x2, as shown in the figure below. Write the area A of the rectangle as a function of x, and determine the domain of the area function. A = all real numbers except x = 36 all real numbers

  2. calculus

    f (x)={cx+d for x≤2 {-x^2−cx for x>2 Let f be the function defined above, where c and d are constants. If f is differentiable at x=2, what is the value of c+d ? -4, -2, 0, 2, 4

  3. Calculus

    At x = 3, the function given by f(x) = { x² , x

  4. calculus

    Suppose f is a one-to-one, differentiable function and its inverse function f^−1 is also differentiable. One can show, using implicit differentiation (do it!), that (f^−1)′(x)=1 / f′(f^−1(x)) Find (f^−1)′(−6) if f(−1)=−6 and

  5. Calculus

    f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(2x)]. The table below gives selected values for f(x), g(x), f '(x), and g '(x). Find the value of h '(1). (4 points) x 1 2 3 4 5 6 f(x) 0 3 2 1 2 0 g(x) 1 3 2 6 5 0 f '(x) 3 2 1 4 0 2

  6. calculus

    Let f be the function defined by f(x)=2x+3e−5x, and let g be a differentiable function with derivative given by g′(x)=1x+4cos(5x). It is known that limx→∞g(x)=∞. The value of limx→∞f(x)g(x) is

  7. math

    Let f be the function defined as: f(x) = (x^2 - 4)/ (x-2) if x≠2 1 if x=2 Which of the following statement(s) about f is true? A. f has limit at x=2 B. f is continuous at x=2 C. f is differentiable at x=2

  8. Calculus

    Sketch the graph of a function that is continuous at x=5 but not differentiable at x=5.

  9. Calculus

    1. The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Left Hand Sum Approximation, using the intervals between those given points. x 10 12 15 19 20 f(x)

  10. Calculus AP

    f is a differentiable function on the interval [0, 1] and g(x) = f(2x). The table below gives values of f ′(x). What is the value of g ′(0.1)? x 0.1 0.2 0.3 0.4 0.5 f ′(x) 1 2 3 –4 5 The answers are: 1 2 4 cannot be determined I got 1 please let me

  11. differentiability

    If g is a differentiable function such that g(x) is less than 0 for all real numbers x and if f prime of x equals (x2-4)*g(x), which of the following is true? A. f has a relative maximum at x=-2 and a relative minimum at x=2, B. f has a relative minimum at

  12. MATH

    Where are the functions f1(x)=|sin(x)| and f2(x) = sin(|x|) differentiable? Use n as an arbitrary integer constant.) f1(x) = |sin(x)| is differentiable for all x ≠______________ f2(x) = sin(|x|) is differentiable for all x ≠______________ No one has

  13. Derivatives

    Determine the interval on which The function is differentiable : f(x) = 3x - 5

  14. CACULUS

    If the function f(x) is differentiable and f(x)= {ax^3 + 6x, if x≤1 {bx^2 + 4, if x>1 then a = What do I do?? No idea what's going on..

  15. Calculus Please Check my answers

    f is a function that is differentiable for all reals. The value of f ′(x) is given for several values of x in the table below. The table: x -8,-3,0,3,8 f'(x)-4,-2,0,4,5 If f ′(x) is always increasing, which statement about f(x) must be true? f(x)

  16. Calculus

    Given that f is a differentiable function with f(2,5) = 6, fx(2,5) = 1, and fy(2,5) = -1, use a linear approximation to estimate f(2.2,4.9). The answer is supposed to be 6.3. Here's what I've done so far: L(x,y) = f(2,5) + fx(2,5)(x) + fy(2,5)(y) L(x,y) =

  17. Mathmatics

    Let f be the function defined by f(x)=2x+3e^−5x, and let g be a differentiable function with derivative given by g′(x)=1/x+4cos(5/x). It is known that limx→∞g(x)=∞. The value of limx→∞f(x)/g(x) is

  18. Calculus

    1. Provide an example of a function f that is continuous at a = 2 but not differentiable at a = 2. 2. Provide an example of a function g that is differentiable at a = 3 but does not have a limit at a = 3. Thanks!

  19. Math

    The twice–differentiable function f is defined for all real numbers and satisfies the following conditions: f(0)=3 f′(0)=5 f″(0)=7 a)The function g is given by g(x)=e^ax+f(x) for all real numbers, where a is a constant. Find g ′(0) and g ″(0) in

  20. Math

    The function f(x)=x^2-ax if x is less than or equal to 1 and f(x)=ax+b if x is greater than 1 where a and b are constants. If f is differentiable at x=1 then a+b= A.-3 B.-2 C.0 D.2

  21. 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

  22. 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,

  23. Calculus

    A differentiable function called f(x) achieves its maximum when x=0. Which of the following must then be true? 1. The function p(x) = xf(x) has a critical point when x = 0. 2. The function m(x) = (f(x))^2 has its maximum at x = 0. 3. The function j(x) =

  24. calc

    Which of the following statements would always be true? I. If f is differentiable at x = c, then f is continuous at x = c. II. If f is continuous at x = c, then f is differentiable at x = c. III. If f is not continuous at x = c, then f is not

  25. 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.

  26. Math

    Find the value of b, if any, that will make the function differentiable at x = 0 g(x)= { x+b, x

  27. Calculus

    Let f be the function defined by f(x)=2x+3e^(−5x), and let g be a differentiable function with derivative given by g′(x)=1/x+4cos(5x). It is known that limx→∞g(x)=∞. The value of limx→∞f(x)/g(x) is

  28. math

    If g is a differentiable function such that g(x) < 0 for all real numbers x and if f'(x)=(x2-4)g(x), which of the following is true?

  29. Math

    Where are the functions f1(x)=|sin(x)| and f2(x) = sin(|x|) differentiable? Use n as an arbitrary integer constant.) f1(x) = |sin(x)| is differentiable for all x ≠______________ f2(x) = sin(|x|) is differentiable for all x ≠______________

  30. Math11

    Hello, I don't know how to do this, please help. Thank you. 1).Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 5x2 − 3x + 2, [0, 2] Yes, it does not matter if f is continuous or differentiable, every

  31. Caclulus

    Suppose f is a one-to-one, differentiable function and its inverse function f−1 is also differentiable. One can show, using implicit differentiation (do it!), that (f−1)′(x)=1/f′(f−1(x)) If f(4)=5 and f′(4)=2/3, find

  32. 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

  33. another graph - complicated

    Sketch the graph of a differentiable function y = f(x) with the following properties. f(2) = 3, f'(2) = 0, and (a) f'(x) > 0 for x < 2, f'(x) < 0 for x > 2 (b) f'(x) < 0 for x < 2, f'(x) > 0 for x > 2 (c) f'(x) < 0 for x not equalt to 2 (d) f'(x) > 0 for x

  34. Math (Function differentiable)

    Determine whether the function is differentiable at x=2 x^2+1 for x2 I did the math for the limits of both equations and they both approach to 4. So that means they are differentiable right?

  35. Math

    f(x)=x/e^x Show that f is continuous and differentiable for all real numbers.

  36. calculus

    sketch graph of a function f that is differentiable and that satisfies the following

  37. Algebra

    1. How many real solutions does the function shown on the graph have? The graph is following the function: y=(x+2)^2 A. No real solutions B. One real solution** My answer C. Two real solutions D. Cannot be determined 2. What is the solution to 3x^2+3x+5=0?

  38. Calculus

    A differentiable function f(x,y) has the property that f(2,2)=2 and fx(2,2)=1 and fy(2,2)=2. Find the equation of the tangent plane at the point on the surface z=f(x,y) where x=2, y=2.

  39. calculus ap

    If g is a differentiable function such that g(x) is less than 0 for all real numbers x and if f'(x)=(x2-4)g(x), which of the following is true?

  40. Math

    which points of f(x)=arcsin(sinx) are not differentiable? And what is the range of this function? How could I do this without graphing? I am just afraid that my test, which does not allow calculators, will have some question asking me to find this

  41. Calculus

    For the following function, find the values of the constants 𝑎 and 𝑏 for which the function is continuous, but not differentiable. 𝑓(𝑥)={𝑎𝑥+𝑏,𝑥>0 & sin𝑥,𝑥≤0.

  42. Calculus

    Assuming that f and g are functions differentiable at a (though we do not know their formulas). Prove that f +g is differentiable at a using the definition of the derivative.

  43. math 116

    What is the difference between domain and range? The domain of a function is the set of all values for the independent variable (in the following example, that's the x) for which the function is defined. That is, if you have a function such as f(x) = 1/x

  44. Calculus

    Here is a graph of the derivative y’ of a continuous, differentiable function. For approximately what values of x between -5 and 5 does the original function y have inflection points. Is it 4 inflection points? paste.pics/fa14942466016d4a8e4a0678cf9d8cbb

  45. Calculus Finals Review sheet!! Explanation needed

    Here is a graph of the derivative y' of a continuous, differentiable function. For approximately what values of x between −5 and 5 does the original function y have inflection points? Find limit as x approaches 3.5 [[x-2]]/x (Remember that

  46. need help i don't understand

    "If y is a differentialble function of u, u is a diffferentiable function of v, and v is a differentiable function of x, then dy/dx=dy/du *du/dv *dy/dx

  47. Calculus

    find all values of x for which function is differentiable. y=lnx^2 why is the answer= for all x doesn't equal 0?

  48. Calculus help

    f is a function that is differentiable for all reals. The value of f ′(x) is given for several values of x in the table below. x –8 –3 0 3 8 f ′(x) 5 4 0 –2 –4 If f ′(x) is always decreasing, which statement about f(x) must be true?

  49. Calculus

    f is a differentiable function on the interval [0, 1] and g(x) = f(2x). The table below gives values of f '(x). What is the value of g '(0.1) x| .1 .2 .3 .4 .5 f'(x)| 1 2 3 -4 5 So I know f(x) would be the integral of f'(x) which you can get with a Riemann

  50. Algebra

    The vertex of a parabola is at (-2,4), and the x-intercepts are at -6 and 2. Determine the domain and range of the function. a. D: all real numbers R: all real numbers b. D: all real numbers R: y ≤ 4 c. D: -6 ≤ x ≤ 2 R: y ≤ 4 d. D: x ≤ 4 R: all

  51. calculus

    Suppose f is a one-to-one, differentiable function and its inverse function f−1 is also differentiable. One can show, using implicit differentiation (do it!), that f(^−1)′(x)=1/ f′(f^−1(x)) Find (f^−1)′(−4) if f(5)=−4 and f′(5)=2/7.

  52. calculus

    a) Obtain all solutions of the equation z^3 +1 = 0 b) Let z = x + iy. Obtain the real and imaginary parts of the function f(z) = 1/1+z c) Let f(x + iy) = x^2 - y^2 + iv( x,y). Determine a function v such that f is differentiable in the whole complex plane.

  53. Calculus

    Use the graph of f(x)=x^2/(x^2-4) to determine on which of the following intervals Rolle’s Theorem applies. A. [0, 3] B. [-3, 3] C. [-3/2, 3/2] D. [-2, 2] E. none of these I know what the Rolle's Theorem is but I'm unsure on how you know if the function

  54. Calculus

    Piecewise function problem. Let f(x)={ax^2+1/3, x is greater than or equal to 1; bx-10/3, x

  55. calculus

    If g is a differentiable function such that g(x) is less than 0 for all real numbers x and if f'(x)=(x2-4)g(x), which of the following is true? f has a relative maximum at x=-2 and a relative minimum at x=2, f has a relative minimum at x=-2 and has a

  56. Calculus (Limits)

    f(x) is a function differentiable at x=1 and f′(1)=1/13. What is the limit of (x^3 - 1)/f(x) - f(1) as x approaches 1?

  57. calculus

    Determine whether y is differentiable at x=0 . If it is differentiable, find the derivative at x=0 . y = {x if x0} y' = ( 1 if x0) Yes , it is differentiable at 0. Is the derivative at x=0, 1?

  58. math

    find the numerical deriviative of the given function at the indicated point. use h=0.001. is the function differentiable at the indicated point? 4x- x^2, x=0

  59. Last two CALC questions. :)

    8. If f(x) = sin(7 − 5x), find f′(π), which is the derivative at π: −0.754 −0.657 0 * 0.657 3.770 9. Given the function: g(x)={x+b, x

  60. Math

    Is the step function differentiable in its domain? I answered it and said that the step function is not differentiable in its domain because it is not continuous. For the a function to be differentiable it would need to have a value and a limit. However,

  61. Calculus

    Let f be a function such that f(−6)=−6, f(6)=6, f is differentiable for all real values of x and −1≤f'x≤1 for all real values of x. Prove that f(x)=x for all −6≤x≤6 I tried applying the mean value theorem here but I'm not sure where to

  62. Maths

    Let f be a function such that f(−6)=−6, f(6)=6, f is differentiable for all real values of x and −1≤f'x≤1 for all real values of x. Prove that f(x)=x for all −6≤x≤6 I tried applying the mean value theorem here but I'm not sure where to

  63. Math--Calculus

    I'm having a tough time figuring out this problem... S(x) = bracket (piecewise function) a + b arcsin*(tan x/tan 66) for 0 ≤ x < 66 24 for 66 ≤ x ≤ 90. Is the function differentiable? Why or why not? Could someone please help me? My teacher told me

  64. maths

    prove that the following function is differentiable at x=0 using first principles: f(x)= e^x when x0 or x=0 also is f(x) differntiable for all real x?

  65. mean value theorem

    Show that the function f(x)=1-|x|, [-1,1] does not satisfy the hypotheses of the mean value theorem on the given interval. Also how do I graph the function together with the line through the points A(a,f(a)) and B(b,f(b)). Also how do I find values of c in

  66. Calculus

    Show that the function f(x)= x^(3) +3/(x^2) +2 has exactly one zero on the interval (-infinity, 0). So far this is what I have: 0=x^3 + 3/(x^2) +2 -2= (1/x^2)(x^5 + 3) -2x^2= x^5 +3 But now I'm stuck. I also am not sure if this is how I'm supposed to be

  67. calc again!

    i got answers for this one, but i feel like i did something wrong. f(x)= 2x+1 when x is less than or equal to 2 (1/2)x^2 + k when x is greater than 2 1) what value of k will make f continuous at x = 2? my answer: i got k = 3 because it would make the two

  68. General Calculus Question

    On a graph what ways can it not be differentiable? I know at cusps it's not differentiable but are there other instances where it is not differentiable?

  69. Calculus

    Suppose f(x) is a differentiable function with f(-1)=2 and f(2)=-1. The differentiable function g(x) is defined by the formula g(x)=f(f(x))' A. Compute g(-1) and g(2). Explain why g(x)=0 must have at least one solution A between -1 and 2. B. Compute g'(-1)

  70. AP Calculus

    Let f be a differentiable function with f(-3)= 1 and f'(−3)= 1 and f'(-3)= -5 Let the function g(x)=3[f(x)]^2 Write the equation of the line tangent to the graph of gg at the point where x= -3

  71. calculus

    Consider the function f(x) = 3-3 x^{2/3} on the interval [ -1 , 1 ]. Which of the three hypotheses of Rolle's Theorem fails for this function on the inverval? (a) f(x) is continuous on [-1,1]. (b) f(x) is differentiable on (-1,1). (c) f(-1)=f(1). Answer:(

  72. math

    Suppose that a

  73. math

    Each of the following statements is false. Provide why the statement is false. 1) Every function that is continuous at x=a is differentiable at x=a. 2) The tangent line to y=f(x) when x=x0 is given by y=fprime(x0)x+f(x0). 3) The linerization of a function

  74. factoring

    can this equation be factored further? y= x^4+2x^3+4x^2+8x+16 Not in the real number system. If you plot the function, you will see the minimum is at x=-1.1 (approx) and y is positive. At no x does the function equal zero, so there are no real roots, which

  75. calculus (hint?)

    f(x) is a twice differentiable function such that f(2x)=f(x+5)+(x−5)^2 What is f''(x)?

  76. calc

    x^2 + √(x+y) + y^2 = 0; y is a differentiable function of x

  77. Math- steve? reiny?

    1. Let f(x)=x^5 + 2x^3 + x - 1 Find f^-1(3) and (f^-1)'(3)? I have zero idea how to find the inverse of this function at a point 3, and how to take derivative of an inverse. 2.Let f(x)=cosx + 3x Show that f(x) is a differentiable inverse and find f^-1(1)

  78. Calc 1

    If a function is continuous, then it is differentiable.

  79. computer science

    Can you find the reason that the following pseudocode function does not return the value indicated in the comments? // The calcDiscountPrice function accepts an item’s price and // the discount percentage as arguments. It use those // values to calculate

  80. Maths

    If f(x)= max{-x-2,-1,x-2} Tell this function is differentiable and continuous at (1,-1)????

  81. Maths

    f(x)is a function differentiable at x=1 and f'(1)=1/8. what is the value of f(x)-f(1) f'(x) denotes the derivative of f(x)

  82. Algebra

    f(x) is a function differentiable at x=1 and fŒ(1)=1/8. What is the value of f(x)-f(1) f'(x) denotes the derivative of f(x)

  83. Math

    Hey I have a question, what does is mean when a function is/not differentiable? thank you.

  84. Calculus

    What is the state of the function f at x = 2? F(x) = [x^3 for x < 2; 5x - 2 for x > or = to 2] ?continuous or differentiable both or neither one or the other?

  85. calculus

    Describe all of the different ways a function may not be differentiable at the point P (a,f(a)).

  86. Math

    Find the value of b, if any, that will make the function differentiable at x = 0 g(x)= { x+b, x

  87. Math

    Find the value of b, if any, that will make the function differentiable at x = 0 g(x)= { x+b, x

  88. calculus

    In the following problem, suppose f(x) is continuous (and differentiable) function on the interval (0,1). Suppose also that for 0 < x>please show steps

  89. Calculus

    Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. If Rolle's Theorem can be applied, find all values of c in the open interval (a,b) such that f'(x)=0. f(x) = x^(2/3) - 1 [-8,8] I plugged in both values and found out that

  90. Calculus

    Given f'(x)=9/2x(3x^2+2)^1/2 (this is the derivative of y= sqrt[(3x^2+2)^3]) , state any values of x for which the function is not differentiable

  91. Calculus

    Prove that there is no function F that is differentiable everywhere and also satisfies the equation F( x^2+ sin(x) ) = x

  92. calculus

    F. (7) (2 puntos posibles) Let f(x)={tanxax+bπ/4

  93. Calculus

    Prove that there is no function F that is differentiable everywhere and also satisfies the equation F(x^2+sin(x))=x.

  94. Math

    Find d^2y/dx^2 at point P(2,1) if y is a differentiable function of x satisfying the equation: x^3+2y^3=5xy

  95. Calculus help

    f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(5x)]. The table below gives selected values for f(x), g(x), f '(x), and g '(x). Find the value of h'(1). x 1 2 3 4 5 6 f(x) 0 3 2 1 2 0 g(x) 1 3 2 6 5 0 f '(x) 3 2 1 4 0 2 g '(x) 1 5

  96. Math

    True or false. Let f(x) be a differentiable function, such that f(0)=−3 and f(3)=−3. Then there exists a c with 0≤c≤3 such that the tangent line to y=f(x) is horizontal at x=c

  97. calculus

    sketch graph of a function f that is differentiable and that satisfies the following conditions:(1)f'(x)>0, when x

  98. Calculus

    1.a)Determine dy/dx if y= sqrt[(3x^2+2)^3] For this question, I got 9/2x(3x^2+2)^1/2 as my answer. b)State any values of x for which the function is not differentiable

  99. Calculus Help Please!!!

    Consider the function f(x)= x −1≤ x< 0 f(x)=tan(x) 0≤ x ≤ π/4 a. Draw a neat sketch of this function. b. Is f(x) continuous at x = 0? (Justify your answer.) c. Is f(x) differentiable at x = 0? (Justify your answer.) show steps! Thanks!

  100. Calculus

    f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(3x)]. The table below gives selected values for f(x), g(x), f '(x), and g '(x). Find the value of h '(1) Numerical answers expected! x 1 2 3 4 5 6 f(x) 0 3 2 1 2 0 g(x) 1 3 2 6 5 0

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