Use the Intermediate Value Theorem to show that the graph of f (x) = 2* – x² intersects the line y = between x = 0 and x = 2.

Q: Let f(x)=x² -3x+5. Show that the average rate of change of f (with respect to x) on an arbitrary…

A: Average rate of change = (f(b)-f(a))/(b-a) Instantaneous rate of change =f'(a+b/2)

Q: 3. Use the first derivative test to locate all local extreme for f(x) = x - 9x2 + 24x

A:

Q: Use Second Derivative Test to find the location of all local extrema for f(x) = 2x³ + 15x² + 24x – 3

A: We Know that The second derivative may be used to determine local extrema of a function under…

Q: USE THE SECOND DERIVATIVE TEST To FIND LOCAL EXTREMA OF THE FUNCTION. F(x)= -x³ +12x² -5ON R.

A:

Q: find the tangent line of f(x)= 3x-4/x+1 at x=0

A:

Q: Find an equation of the tangent line to the graph of y = f ( x ) at the point on the graph where x…

A:

Q: Find all relative extrema of the function f(x) = x* – 4x2 + 2 by using the Second Derivative Test…

A: Given, The function  fx=x4-4x2+2 We have to find the all relative extrema of the function using the…

Q: Find all relative extrema of the function f(x) = x* – 4r +2 by using | the Second Derivative Test…

A:

Q: Use the first derivative test to locate all local extrema for 3 f (x) = -x'+ = -x' +- x +18x.

A: Explanation of the answer is as follows

Q: apply 1rt and second derivative to sketch graph  1)f(x)=3+7e^(-0.2x) and  2)f(x)=ln(2x+4)

A: In the question we have to draw the graph.

Q: 3. Is the function given by x²-4x-5 -,x< 5 f(x) =. x-5 x+1, x 2 5 continuous atx=5? Why or why not?

A:

Q: Use the Second Derivative Test to find all relative extrema. h(t) = -x + 6x² - 4

A:

Q: tion of the tangent line to f(x) = 4 %3D

A:

Q: Use the first derivative test to find and classify the relative extrema of x2 +8x+ 16 f(1) = For…

A:

Q: 1 F(x) = -1. tanh 3x

A:

Q: 13 Use the power rule to find the derivative of f(x) = Vx. %3D f'(x) =

A:

Q: Use the second derivative test to find the extre #1) f(x) = x³ + 2x² - 4x-8 %3D

A:

Q: Please help. *Find the equation of the normal line (NL) to the graph f(x)=x³-4x at x = 3. *For…

A: To find the equation of normal line to the curve

Q: how would you, using a limit def. of a derivative at a point find f'(-1) for the function f(x). =…

A: Hint:

Q: Use the second derivative to find the location of all local extrema for f (x) = x + x2 – x3, -

A:

Q: find all possible functions with the givenderivative. y' = √θ - sec2 θ

A: Given: y'=dydθ=θ-sec2θ for evaluating solution of given differential equation, we use variable…

Q: 9) Use the second Derivative Test to find all relative extrema. f( x) = - (x + 2)°(x – 4)?

A: Find f'(x) and solve for x by putting f'(x)=0.

Q: Calculate the derivative for f(x) = (x + 3)(x – 1)(x – 4). (Use symbolic notation and fractions…

A:

Q: 8 Use the power rule to find the derivative of f(x) = x°. f'(x) =

A:

Q: find the derivative of f (x) at the designated value of x. f (x) = 1/x at x = 2/3

A: Given: f(x)=1x To find the derivative at x=23

Q: Consider Mean Value theorem for derivative for function f(x) 4(1-2x) in interval [0,1]. TCOS(TX) -

A:

Q: Use Second Derivative Test to find the location of all local extrema for f(x)=2x³+21x²+36x-1

A: Local extrema.

Q: Find f'(x) from f(x)= = 2x³x²x+ 2 using the definition of a derivative. (Do not include "f'(x) =" in…

A: Use simple differentiation formula.

Q: Find an equation of the tangent line to the graph of f ( x ) = 2x2 - 10 over 2x - 2 at the point on…

A:

Q: ve of the function using the definition of derivative. = V7- x 1 2 7-x n of the function. (Enter…

A:

Q: 2) Use the definition of the derivative, f'(x) = lim Ax-0 derivative of f(x) = 5x² + 3. f(x+Ax)-f(x)…

A:

Q: 6. Use the definition of derivative to find f'(x) if f(x) 3D х2 — Зх — 4

A:

Q: Find f′(x) from f(x)=2x^3−x^2−x+2 using the definition of a derivative. (Do not include "f′(x)=" in…

A: we have to find f'(x) using limit definition of derivative

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x)=√8x+9 at…

A: Here we have to find the instantaneous rate of change of f(x) = √8x+9 at x=1.

Q: Use Second Derivative Test to find the location of all local extrema for f(x) = 2x3+21x²+ 36x-1

A:

Q: Find the points on the graph of f where the tangent line is horizontal.  f(x)=(x^2+8)(5-x) larger…

A:

Q: Use the second derivative test to find all relative extrema  f(x)= x+4/x

A: The given function is as - f(x) = x+4xProcedure to find local extremas - 1. Find f'(x)2. Put f'(x) =…

Q: Find the points on the graph of f where the tangent line is horizontal. f(x) = x3 - 18x2 (x, y) = (…

A: As we know that the slope of the tangent on a graph represents by f '(x) and it is parallel to the…

Q: Apply the first derivative test to indentify all relative extrema. f(x) = ¹²-2x+1

A:

Q: Find the point on the line y = – 4x + 2 closest to the point (8, 9). - The function giving the…

A: Given, equation of line : y = -4x +2 And  The point : (8, 9) {outside the line}

Q: 5. Use the Second Derivative Test to find all local extrema of the function below. (3 points total)…

A: To find the local extrema of the given function f(x)=x4-4x3+2

Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

A: The given Revenue function R(x)=23x3-40x2-450x.  Task: To maximize this revenue function.

Q: 2. Is the function given by F(x) = x². 5x + 6 continuous over the interval (-5, 5)? Why or why not?

A:

Q: 1. Use the first derivative test to find the location of all local extrema for 3 f(x) = -x³ +x+ 18x…

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: Use the second derivative test to locate all local extrema for the function f(x)=x3−32x2−18x. At…

A:

Q: Differentiate the functions showing the general process in determining the derivatives. Using the…

A: We need to differentiate given function.

Q: 7 Use the power rule to find the derivative of f(x) = x f'(x) =

A: Power Rule: The power for the derivative of the function xa is given by, The given function is f(x)…

Q: A company has identified that the revenue R for a particular product is given by the equation R(x) =…

A:

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) 7x² + 2x…

A:

Q: What is the average rate of change of f(x)= x2 -2 on the interval [-1,3]?

A: