# Math - Derivative of a polynomial function(check)

162,736 results

### Math - Derivative of a polynomial function(check)

The red squirrel population, p, in a neighborhood park can be modelled by the function p(t)= srqt(210t+44t^2), where t is time in year. a) Determine the rate of growth of the squirrel population at t= 2years Ans: find the 1st derivative and substitute 2 in the function. b) ...

### 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 derivative they reach the ...

### Math:Polynomial Functions

h(x) = -7x I was thinking that this was not a polynomial function because -7x is just one term making it a monomial but the answer key says it is a polynomial function. Could someone explain why that is so? Thanks :D

### Math

The function f(x) = x^2 -2x + x^1/2 is: A. A polynomial because it is continuous. B. A polynomial because it is of the form axn. C. Not a polynomial because you are subtracting 2x. D. Not a polynomial because you can’t have any fractional exponents. Is the answer D?

### 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

### Math

What does the degree of a polynomial expression tell you about its related polynomial function? Explain your thinking. Give an example of a polynomial expression of degree three. Provide information regarding the graph and zeros of the related polynomial function.

### Math

Can you please check my answers. Determine whether the function is a polynomial function. f(x) = 4x + 4x^5 -Yes f(x) = 4 - 1/x^2 -No

### Polynomial Function

Could you please check my answers? Find an nth degree polynomial function with real coefficients satisfying the given conditions. 1. n=3; 3 and i are zeros; f(2)=20 -I got: f(x)=-4^3+12x^2-4x+12 3.n=3;4 and i zeros;f(-3)=60 -I got:f(x)=6x^3+24x^2+6x+24

### 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 derivative tell you ...

### calculus

f(x) = 6x^2 -8x +3 how would I find the most general antiderivative of the function. I also have to check my answer by differentiation. Would I have to find the derivative first? (I got 12x -8) What are the steps to solving a problem like this? No, don't do the derivative ...

### 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 evaluated in 9] . I don...

### polynomial function

Please check my answers. Find the y-intercept of the polynomial function. f(x) = -x2 - 2x + 8 I got:y=8 f(x) = (x + 1)(x - 6)(x - 1)2 I got: y=-6 f(x) = -x2(x + 6)(x2 - 1) I got:y=0

### Math - polynomial function

Write a polynomial function with integral coefficients having the given roots. 1.) 0, -1/2, 6 2.) +or- 5i

### 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 =, the derivative is ...

### 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?

### math

Is the function a polynomial function? Why or why not? If it is a polynomial function identify and label the leading term and constant term. Here are the functions f(x)=(2-x^4)/13 f(x)=x^3+9x-(1/x) it would be great if you could do everything step by step and showing your work.

### 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 zeroes of the graph of ...

### 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 second derivative rule ...

### 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 second derivative rule ...

### 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)

### Graphs of polynomial functions

What do polynomial functions look like? And what can be consider a polynomial function? Would a graph that is like an upside down V be considered as a graph of a polynomial function?

### Math

Suppose you have a graph of a polynomial function and you can see that the function increases without bound on both left and right ends, has 4 real zereos and has 5 turning points. Based on this information, what is the minimum degree of the polynomial?

### Polynomial Functions

What do polynomial functions look like? And what can be consider a polynomial function? Would a graph that is like an upside down V be considered as a graph of a polynomial function?

### Polynomial Functions-help

What do polynomial functions look like? And what can be consider a polynomial function? Would a graph that is like an upside down V be considered as a graph of a polynomial function?

### Math - Derivative of a polynomial function

The population, p in thousands of bacteria colony can be modelled by the function p(t)=200+20t-t^2, where t is the time, in hours, t is greater than or equal to zero. a) Determine the growth rate of the bacteria population at each of the following times. i>3h ii>8h Ans: ...

### Math - Derivative of a polynomial function

A flaming arrow is shot into the air to mark the beginning of the a festival. Its height, h, in meters after t seconds can be modelled by the function h(t)=-4.9t^2+24.5t+2 How fast is the arrow traveling when it hits the ground? Explain how you arrived at your answer. (prior ...

### 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 multiply that by ...

### 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 have a quiz on them ...

### 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 second derivative rule ...

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= log10(1 + 1/x) y'= ((1/(1...

Please check my answers and let me know if I did something wrong. Thank you! Find the partial derivative of x, and the partial derivative of y, then the partial derivative of x (1,-1), and the partal derivative of y (1,-1). f(x,y) = x^4 y^2 -x here is what I got @f/@x = 3x^3 y...

### Polynomial Function

Could you help me with the following problem, I don't understand how to do it. Find an nth degree polynomial function with real coefficients satisfying the given conditions. 1. n=3; 3 and i are zeros; f(2)=20

### 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 equation. Isn't the ...

### Math

How can I determine a value of gradient from a graph if the line is curved. (not a straight line) This is where Calculus comes in If a graph is a curve, then the gradient (slope) of the curve is the slope of the tangent that you draw at a particular point on that curve. You ...

### math

Create a quadratic polynomial function f(x) and a linear binomial in the form (x − a). Part 1. Show all work using long division to divide your polynomial by the binomial. Part 2. Show all work to evaluate f(a) using the function you created. Part 3. Use complete ...

### 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= log10(1 + 1/x) y'= ((1/(1...

### Algebra

Please check my answers. Thanks! Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. 5.2x^3-13x^2+22x-8=0 -My answer:{1/2,2,4} 6.x^3-8x^2-x+8=0 -My answer: {1,-1,8} Find the rational zero of the ...

### 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 function is decreasing at x...

### 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 different when using log ...

### Calculus

A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx + k? A cubic polynomial function f is defined by: f(x) = 4x^3 + ax^2 + bx + k where a, b, and k are constants. The function f has a local minimum at x= -1, and the graph of f has a point of inflection at x= -2...

### Calculus

A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx + k? A cubic polynomial function f is defined by: f(x) = 4x^3 + ax^2 + bx + k where a, b, and k are constants. The function f has a local minimum at x= -1, and the graph of f has a point of inflection at x= -2...

### Math

0.08x^3 + 0.6x+2.8 absolute-value function Rational function Another polynomial function Quadratic function

### math

How is the range of a polynomial function related to the degree of the polynomial?

### Math

How do you divide a polynomial function by another polynomial function.

### 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 problem is cos*2*pi*) is ...

### calc

find the values of a nad b if the function f(x)=2x^3 + ax^2 + bx + 36 has a local max when x=-4 and a min when x=5 First you calculate the derivative: f'(x)=6x^2 + 2ax + b (1) At the local maximum and minumum f' is zero. If a polynomial is zero at some point p, then it must ...

### 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 power rule, quotient...

### Math - derivative of a rational function

find the 1st derivative of f(x) = x/(x-1)2 Is the 1st derivative f'(x)= -x-1/(x-1)^3

### 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 decreasing. Now by ...

### 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 instead integrate the ...

### 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 derivative of sin(x)*e^(ax...

### 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 derivative dy/dx = 8x^3 - ...

### Calculus

I need to find the second derivative of y=x(x-1)^1/2. I found the first derivative is 2x-1/2(x-1)^1/2, if someone could check, but I am miserably stuck on the second derivative.

check my answers please. Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. f(x) = 2x3 + 10x2 - 8x - 5; between 1 and 2 -I got: f(1)=1 and f(2)=35;no Determine the maximum possible number of turning ...

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?

### 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 original form look different...

### 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)?

### 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 taking it again? Is it ...

### calculus totally confused

find a first degree polynomial function p(1) whose value and slope agree with the value and slope of f at x=c. i think you use taylor series for this f(x)=4/sqrt(x), c=1 i'm totally confused on how to do it. i know you find the derivative but how do i get the function. this is...

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 points. 2. Find dy/dx ...

### Calculus

Please.... I need your help! I posted this question yesterday and no one has answered it yet. Can anyone help me please? My question was: The Taylor series about x=5 for a certain function f converges to f(x) for all x in the interval of convergence. The nth derivative of f at...

### 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 derivative of each of...

### Math

1. Identify the degree, leading term and leading coefficient of each polynomial function. A. f(x)= x(x+1)(3x+1)(x-2) B. f(x)= -16+3x^4 - 9x^2 - x^6 + 4x^8 2. Describe the end behavior of a ninth-degree polynomial function with a negative leading coefficient.

### calculus

At the indicated point for the function, find the following. A graphing utility's numerical derivative feature can be used to check your work. y = (x3 + 2x)3 at x = 3 (a) Find the slope of the tangent line. (b) Find the instantaneous rate of change of the function.

### 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 negative, the ...

### math

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

### 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 derivative gives you points ...

### 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

### 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 = 15x2+120x&#...

### Math - derivative of f(x) (check)

Find the derivative of f(x)=7x-19 at x=2. I think that the derivative would be 7 and theb times 2 so 14. Is this correct or would it just be 7.

### Writing polynomial functions

How to write a polynomial function with the integral coefficients that have the following roots: #1.) 0, -1/2, 6 #2.) + or - 5i

### Graphing polynomial functions

How do i graph the polynomial function of: f(x)= (x+3)(x+1)(x-2) squared

According to the first derivative test, a differentiable function must have a relative minimum between any two relative maxima. True.

### College Algebra

1.Give a quadratic function q(x) with a vertex of (-1, 2). 2. Give a function h(x) which does not have an inverse function. 3. Give a polynomial function g(x) with zeros 1,2,3 4. Give an exponential function s(x) passing through (0,2) and (4,1). 5. Give a rational function R(x...

### 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 10/(7x+10)^2

### Math

True or false Some rational numbers are integers. The radius of a circle and its circumference. Direct or inverse f(x) 0.08x^3 + 0.6x + 2.8 Rational function, another polynomial function Quadratic function

### Math

Some rational numbers are integers. True or false The radius of a circle and its circumference. Direct or inverse f(x) 0.08x^3 + 0.6x + 2.8 Rational function, another polynomial function Quadratic function.

### 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, but I can't find any ...

### Math - Simple rational Function (check)

Consider the function f(x) = x/(x-1) Are there any turning points? Explain how this could help you graph f(x) for large values of x? Ans: turning points is another word for checking the concavity, and therefore i find the second derivative and equate it to zero and see where ...

### math

A polynomial function function is defined by the equation p(x)=3x3+ax2+bx+7, where a, bE/. If p(-2)=5 and p(1)=14 then the value of a+b is...

### math

#1 If v=(6-(r^3/3))h and h/(2-r)=5/2 write V as a function of h . Simplify the function so that you can express it as a polynomial in h . #2 If y=ln(x) , write ln(x^x) as a simple function of y thxs alot!

### Calculus derivatives

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

### 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.

### calculus

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

### 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 how to post integral ...

### 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?

### 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!!

### Calculus

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

### Derivative

if g(x)= 5x^6-3/x^2, find the 3rd and 5th derivative of the function. Pls help!

### Pre-Calc

Fill in the blank; •In the process of polynomial division (Divisor)(Quotient)+_______=_______ •When a polynomial function f is divided by x-c, the remainder is _______. •If a function f, whose domain is all real numbers, is even and if 4 is a zero of f, then _______ is ...

Find all zeros of the following polynomial. Write the polynomial in factored form. f(x)=x^3-3x^2+16x-48 I put: x^2(x-3)+16(x=3) (x-3)(x^2+16) For zeros: x-3=0 x=0 **My teacher stated check the equation solution again. What is the value for x and hence what is the zero for the ...

### 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! :)

### 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 from there? What do ...

### college algebra

let f(x) be polynomial function. explain how to use the factor theorem to check if x) is a factor of F(x)

### 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 that the function g ...

### 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 you retype your ...

### Math

Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use the result to factor the polynomial completely. List all the real zeros of the function. x^3 - 28x - 48 = 0 x=2 I have no idea how to start this problem!!

### Calculus derivative

find the slope m and an equation of the tangent line to the graph of the function f at the specified point. original: x^2/x+10 point: (3,9/13) After I found the derivative: (x+10)(2x)-(x^2)(1)/((x+10))^2 How do I get the slope? Should I put 3 into the derivative equation?