Let f(x)=x^3-3x^2-3x+9. For what values of x is f'(x)=0? What are the local max and min points for f(x)?

Q: 13. f (x) = sinx3 (2х-1)2

A: I have stated the used formulas in the solution

Q: What is the first derivative of s(x)=(7x)3x at x=4?

A: To evaluate s'(4)

Q: find derivative of g(x)=integration3x2x (u2-1)/(u2+1) du

A:

Q: 8. Find the derivative of f (x) = 2tanx – 3secx. Show all steps -

A: We have to find the derivative of the function fx=2tanx-3secx Then,…

Q: When the Second Derivative Test Fails Analyze the critical points off (x, y) = 3xy 2 - x 3 .

A: Given Data The function is f(x,y)=3xy²-xᶟ.   Differentiate the function f(x,y)=3xy²-xᶟ with respect…

Q: Solve for the derivative of the function using chain rule. 9. f(x)= esinx

A: Solve for the derivative of the function using chain rule. 9. f(x)= esinx

Q: Explain how the First Derivative Test determines whetherƒ(x) = x2 has a local maximum or local…

A: Given:   f(x) = x2 To determine whether f(x) has a local maximum or local minimum at the critical…

Q: Find the relative extrema of f(x) = 8+ 126x – 7x2 using both first and second derivative tests. f…

A: If second derivative is less than zero then there is relative maxima.

Q: Use second derivative test, If f(x) = 25x + 10 then f(x) has a 3 local maximum at the point_

A:

Q: Use forward, backward and central difference to estimate the first derivative of f (x) = In at x =…

A: Given function is fx=lnx and x=3 Step size h=0.01 We have to estimate the first derivative of fx=lnx…

Q: 2. Show a graphical method of approximating the instantaneous rate of change at x = 3 for the…

A: You must have idea about what is the basic difference between instantaneous and average rate of…

Q: Use central difference method to estimate the 1st derivative of the following function at x = 2 and…

A:

Q: 2. Determine the second derivative of f(x)= x'e* at x = -2 with a step-size of h=0.50 using Central…

A: Given function is f(x) = x2e2x and h = 0.50

Q: By using the second derivative test for functions of two variables, find three positive numbers…

A:

Q: Find the derivative using DELTA METHOD f(x)= 2x-x2

A:

Q: How to find the critical points of this derivative

A: We have to find critical point of f(x),where f'(x) is given by:

Q: Estimate the root very near x = 0.4 of 4(x*)" - 4(x²) + 1 = 0 using the Newton- Raphson Method with…

A: Consider a function:  fx=4xx4-4x2x+1      =4x4x-4x2x+1

Q: Use forward difference approximation to estimate the first derivative of the following equation.…

A: Given that, fx=-0.15x3-0.2x2-0.5x+2.25h=0.5We need to find the first derivative of the function at…

Q: S(x)= Jx-5

A: given that f(x)=1x-5 find the derivative from first principle f'x=limh→0 fx+h-fxh

Q: Determine if the critical points of the function f ( x ) = x³ + x² - x - 2 are maximum or minimum…

A: The given function is: fx=x3+x2-x-2   As we know that; To calculate the critical point, f'x=0.

Q: Find the critical coordinates of f(x) = x³ – 3x² + 8x + 1. Then, distinguish the local maximum and…

A: Given function is  f(x) = 13x3-3x2+8x+1                 ....(1) Differentiate with respect to x , we…

Q: To investigate these values, we find the second derivative f"(x) = %3D At the positive critical…

A: Given function is : fx=3x-4x3

Q: maximum point of y x – 2

A: Condition for Extreme Value: A continuous function fx, y has extrema at a, b if fx=fy=0 at a, b…

Q: fcx)= Y文 メ ー^

A: Local extrema

Q: Determine the second derivative of f (x) = x²e* at x = -2 with a step-size of h=0.50 using Central…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: The derivative of the function y = etan(4x) is: a) y' = tan (4x)etan(4x) b) y' = 4 sec²(4x) etan(4x)…

A: Given data: The given function is y=etan(4x). Differentiate the given expression with respect to x.…

Q: 2. Determine the second derivative of f(x) = x²e²* at x = -2 with a step-size of h=0.50 using…

A: Given function f(x)=x2e2x. The objective is to determine the second derivative of fx at x=-2 with a…

Q: Find the derivative of f (x ) =V sech( In (8x + 1)) - sech(In(8x + 1)) tanh( In(8x + 1)) A 2/ sech(…

A:

Q: Approximate the derivative of f(x) = x² + 4x + 5 at x = 3 using the forward, backward, and central…

A: f(x) = x2 + 4x + 5 h = Δx = 2 xi = 3         f(xi) = 26 xi+1 = 5          f(xi+1) = 50 xi-1 = 1…

Q: Derive a formula that approximates the second derivative of the function sampled at x = 0, 0.01,…

A: Let us assume that second derivative function  f"x0=Afx0+Bfx0-h+Cfx0+2h can be rewritten as…

Q: Integrate xtanx with respect to x

A: We have to solve this integral by  Integration by parts rule, Formula is  ∫uvdx=u∫vdx-∫u'∫vdxdx

Q: Find the critical value of f (x) = vx² + x – x using the second derivative test. %3D

A:

Q: find any locl maximum and locl minimum values by using first derivative: f(x)-x-2x

A: Given :           f(x) = x4 - 2x2

Q: Find the relative extrema of f(x) = 4+70x – 5x² using both first and second derivative tests. f (x)…

A: Given:- f(x) =4+70x-5x2  To find:- Relative extrema of f(x) using both first and second derivative…

Q: Find the derivative of f(x)  =(a + 2x2) (x - x2) in twoways: by using the Product Rule and by…

A: We have given function  fx=a+2x2x-x2 At first we  will use product rule:…

Q: Show that the function has partial derivative at the point (0,0) but is discontinuous at this point.

A: solve the following

Q: Find the linear approximation of the function f (x,y) = ln (x - 3y) at point (7,2).

A: To find the linear approximation of the function fx, y=lnx-3y at the point 7, 2.

Q: Solve for the derivative of the function using chain rule. 14. f(x)= 3lnx 15. f(x)= cos(cosx))

A:

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

A:

Q: Find the derivative of the following using General Rule. 7) y = vt3 8) f(x) = 6 + 5 1 9) y =-+ 2 x3…

A: We have to find derivative of Given function.

Q: Determine the second derivative of f(x) = x²e²x at x = -2 with a step-size of h=0.50 using Central…

A:

Q: 2. Determine the second derivative of f (x)=xe* at x = -2 with a step-size of h=0.50 using Central…

A: Given f(x) = x2e2x

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: Determine the local extrema for t(x) = -3x3 - N2 - 90x +1 using the First Derivative Test. %3D

A:

Q: find any locl maximum and locl minimum values by using first derivative: f(x)=x*-2x?

A: The given function: f(x)=x4-2x2 To find the first derivative of the function: f'(x)=4x3-4x Now, let…

Q: The function whose derivative is given by f'(x)=(x-¹), x 2. What is the #+2 critical point of f?

A: Critical point of a function is a point where either the derivative of function is zero or not…

Q: 4. Use the first and second derivative to find the absolute maximum and minimum, if either exists,…

A:

Q: 2 12. f (x) = (1tsinx) Cosx

A:

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

A:

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

A: