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

Q: Use the first derivative test and the second derivative test to determine where each function is…

A:

Q: If f (x) = 12 + 2x² – x*, use the second derivative test to find the local extrema of f.

A: Just use second derivative test and answer will follow.

Q: Use the derivative to find for which values of c the function 1 f(x) = CI+ x2 +3

A:

Q: Using the definition of the derivative, find ƒ′(x) . Then find ƒ′(−2) , ƒ′(0) , and ƒ′(3)  when the…

A: The given function is fx=13x The definition of the derivative is shown below: f'x=limh→0fx+h-fxh

Q: Find the derivative of the algebraic function.

A: To Find the derivative of the algebraic function. f(x)=x2+5x+6x2-4

Q: Use the chain rule to find the derivative of f(x) = 6/3x + 5x10 Type your answer without fractional…

A:

Q: Use the second-derivative test, if possible, to find relative extrema of y x5 – 5x. -

A:

Q: Use the chain rule to find the derivative of f(x) = 6/9x*+ 7x³ Type your answer without fractional…

A: Firstly a function is given by, fx=69x4+7x3. The objective is to find the first derivative f'x with…

Q: 1. f(x) = x² at x = 3

A: Given: f(x)=x2 at x=3

Q: Use the chain rule to find the derivative of f(x) = 6/8° + 5x° %3D Type your answer without…

A:

Q: The derivative of the function y -3x2+4 is: %3D sec x

A: Given that y=-3x2+4secx find the derivative of y

Q: Use the first derivative and the second derivative test to determine where each function is…

A: We first find the first and the second derivatives y=-3x2-5x+2dydx=-6x-5d2ydx2=-6

Q: Find the general antiderivative of each function. (can check by taking the derivative) F(X)= 12x3…

A: Antiderivative: Given the derivative of a function, find the function itself. Find the…

Q: find the derivative of f(x) = x2 – 3x + 4, and then 3) evaluate f '(2)

A: Given : f(x) = x² - 3x + 4

Q: Q2/ Find the derivative of the function (x) =v3x-x by definition

A: Solve the limit for very small change in x .

Q: Using the second derivative criterion, find the graphs of the functions a) F(x) = x*– 8x² +3

A: Given- (a)  Fx=x4-8x2+3 To Find- The graph of the above functions using second derivative.

Q: Consider the function x + 5 f(x) : + v2 + 7x 4 – x Use the definition of derivative to find f'(0).

A:

Q: a) Find the derivative of g(x) = 3tanx – 4cotx. %3D b) What is the value of g 3.

A:

Q: f(x)= 2x3 +3 Use definition of derivative to find d/dx f(x)

A:

Q: Find the derivative of f(x) = (v5x – 2)°. Final answer must have no parentheses.

A:

Q: Find the second derivative of function, and then find ƒ″ (1)  and ƒ″ (−3) .

A: given,        fx=1-2x4x+5

Q: Use the first derivative test and the second derivative test to determine where each function is…

A:

Q: Find the derivative of the function. Express the answer using positive exponents only. y = 2/3x3(4x5…

A:

Q: a) Find the derivative of g(x) = 3tanx - 4cotx. b) What is the value of g'() ?

A:

Q: Apply the second derivative test to find the absolute extrema of each function on (0, 0) 6. a) f(x)…

A:

Q: Use the Quotient Rule to find the derivative of the function. 3x - 7 g(x) = %3D x² - 1

A:

Q: function with respect to x. a. f(x) = -4x – 2 b. f(x) = 3x² + 4 c. y = 3x² + 3x + 3

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Use the Quotient Rule to find the derivative of the function.                                f(x) =…

A:

Q: f (x)=vx+2, a=6 it

A: Given function is  fx=x+27

Q: Use the Quotient Rule to find the derivative of the function. 2х — 3 g(x) x - 1 g'(x) = %3D

A: Given that gx=2x-3x2-1

Q: f(x) = 3x2 + 1

A:

Q: Use the First Derivative Test to find the local maximum and minimum values of the function. y = 2x2…

A:

Q: Use the second derivative test to find the extreme values of the function 49 f(x) = 25x +

A:

Q: f(x) = V4x +5 , use the definition of the derivative to find f '(x).

A:

Q: Using the definition of derivative, find the derivative of f(z) = x + 5x + 5. %3D

A:

Q: Use the first derivative and the second derivative test to determine where each function is…

A: Given that,y=x3-5x2+8x+4   , x∈ℝ y'=dydx=ddxx3-5x2+8x+4    =3x2-10x+8    =3x2-6x-4x+8    =3xx-2-4x-2…

Q: 2) Use the second derivative test to find the local extreme values of y= x5 – 5x³+7

A: Given that, We will find the local extreme values of the function as following.

Q: Use the first derivative test and the second derivative test to determine where each function is…

A: The given functions y=2x-313 Differentiate with respect to x f'x=132x-313-1…

Q: t(x)=23x3−10x2+42x+9 Given the function above, use the First Derivative Test to find the local…

A:

Q: f(x) = 2x² + 7x – 6. Find the first derivative of f(x) using the definition.

A:

Q: . Use derivative rules to find the derivative of h(x) = 3f(x) – 2g(x) – x² f (x) +. Show steps g(x)

A: See attached file for a step by step explanation.

Q: Use the chain rule to find the derivative of f(x) = 10/6x10 + 8x° Type your answer without…

A:

Q: Using the second derivative criterion, find the graphs of the functions b) F(x) = x³/3 - 9x + 3

A:

Q: Find the Derivative f(x) = X3In x

A: The derivative of f(x)=X3lnx ddx(x3lnx)Apply product…

Q: Use the definition of the derivative to find df/dx. f(x) = x/(1-3x)

A: Given, function

Q: Find all possible functions with the given derivative. 7) y' = 5x2 + 1 %3D

A: solution = y' = 5x2 + 1  y' = dy/dx dy/dx = 5x2 + 1 ∫dy = ∫(5x2 + 1 ) dx + c  [ yn dy = yn+1 ] y…

Q: Use the Second Derivative Test to find all local extrema, if the test applies. Otherwise, use the…

A:

Q: Use the General Power Rule to find the derivative of the function. g(x) = V3 - 9x %3D g'(x) =

A:

Q: a) Use the definition of the derivative to find f '(x), given f(x) = 4x² – 1.

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

Q: Use the second derivative test to find the extreme values of the function f(x) = 49x + 1. Answer:

A: Second Derivative Test for Local Extrema The second derivative may be used to determine local…