250 4. Use second derivative test to determine the relative extrema of the function: f(x) = x2 +

Q: use definition to show that the function f(x)= |x|^3 is differentiable at 0, with derivative equal…

A: We have to use definition of differentiable:

Q: Find the first and second derivatives of the function. f(x) = In(x + 4) f'(x) = f"(x) I3D

A:

Q: Find the second derivative of the function. 10. f(x) = 4x3/2 11. g(x) = x-1 12. h(x) = sec x

A:

Q: 16. Use the definition of the derivative to find the derivative of the function f(x) = 3/x and g(x)…

A: Given,

Q: Determine the derivative of f(x) = 3 x2 In x with respect to x. f '(x) :

A: We differentiate both sides with respect to x and apply the rule d/dx(uv)=ud/dx(v)+vd/dx(u)

Q: Find the derivative of the algebraic function.

A:

Q: 1 Use the power rule to find the derivative of f(x) = Vx 15 f'(x) = %3D

A:

Q: Find the derivative of the algebraic function.

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

Q: Find the absolute extrema of the function f(x) = (x + 16) 1/3 on the interval[-5,2]. Find the second…

A: To find  The absolute extremum of the given function.

Q: Use the first derivative test to determine the local extrema, if any, for the function f(x) = 3(x -…

A: Given that a function f(x) and we find local extrema. For local extrema we do first derivative of…

Q: Find f'(x) using the definition of the derivative. 1. f(x)=x^3-1

A: We have given f(x) = x3-1 So using definition of derivative  f'(x) = limh→0fx+h-fxh So f(x+h) =…

Q: Determine the derivative of f(x) = 3 x² In x with respect to x. f'(x) = |

A: We have to find f'(x)

Q: 5. Use the definition of derivatives to find f'(2) given that f(x) = 2x² -r+1

A: According to our company guidelines we are supposed to answer only one question since you have asked…

Q: 16) Find f'(x) using the definition of the derivative. f(x) = x3 + x

A:

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

A:

Q: Find the absolute extrema of the function f(x) = (x +9) 2/3 on the interval [-5,1]. Find the second…

A: To find absolute extremum of given function:

Q: Let f(x) = (x² + 3x)e*. Determine the value of the third derivative of f(x) for x = 0.

A:

Q: Find the derivative of the function. (x) = In(4 – x®) r"(x) =

A: We have to find

Q: Can you help me step by step?

A: The given function is,

Q: Find the derivative of the function f(x) = 8x2 – 13x by the definition of derivatives f(x + h) –…

A: on using this formula we get = 16x-13

Q: Find the derivative of the function. f(x) = (x2 + 3) In(x) f'(x)

A:

Q: Find the derivative of the algebraic function.

A: The given function is fx=x41-2x+1.

Q: 3 Use the definition of derivative to find f'(x) for f(x): II

A: Given:

Q: Use the first derivative test to determine the relative extreme values of the function. below. a.…

A:

Q: 16. Use the limit definition of the derivative to find the instantaneous rate of change for the…

A:

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

A:

Q: Let f(x) = }x² – x³. Find the value(s) of x if the second derivative f" (x) equals zero.

A: Use the formula, ddx(xn)=nxn-1 to calculate the derivative. Differentiate f(x) with respect to x to…

Q: Consider the function f(x) whose second derivative is f''(x)=8x+10sin(x). If f(0)=3 and f'(0)=2 what…

A: The function is f"x=8x+10sinx.   Integrate the function.…

Q: 1. Evaluate the derivative of f (x)= sec(In(x²)). DO NOT SIMPLIFY.

A:

Q: 5. What is the definition of the derivative of a function f(x) ?

A:

Q: (a) Use the definition of the derivative to calculate the first derivative f'(x) for the function…

A:

Q: Find the f derivative of x given f(x)=(3x)^-1

A: Calculation:Compute the derivative of f(x) = (3x)−1 as follows.

Q: Find the derivative of the function. f(x) = In x+ 2 f'(x) =

A: We have to find the derivative of the given function.

Q: 12. Find f'(x) using the definition of the derivative.  f(x) = x3+ x

A:

Q: Find the derivative of the function. f(x) = (x² + 8) In(x) f'(x) =

A: In this question we need to find a derivative of the given function

Q: 7. Determine the derivative of the function with respect to x. ソミx

A:

Q: 1. Use the definition of derivative to find the derivative of (a) f(x) = (x + 1)² 1 (b) f(x) =…

A: The solution are next step

Q: 2. Find the derivative of (a) f(x) = x* + 4x 2 + 4e" (b) f(x) = 2 tan (x) – 6"

A:

Q: Let f(x) = x-3 Use the definition of derivative to find f'(x). %3D 2C

A: Given : fx = xx-3

Q: 9. Use the definition of a derivative change of the functions below at f(x)% = x² + 2x

A:

Q: 10 Use the power rule to find the derivative of f(x) = Vx.

A: Given,          The function is fx=x10 .

Q: Find the derivative of the algebraic function.

A: Given, fx=x1-4x+3

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

A:

Q: 10 The derivative of the function f(x) = x7 + - 10 726 + (r³) 10 71° + (2) 1 10 7x + 10 10 726 (z²)…

A:

Q: Use first principles definition of the derivative to find f'(x) for the function 3 f(x)= x-2 =

A:

Q: Use the first derivative test to determine the relative extreme values of the function. below. a.…

A: local minima or relative minima is a point on the x-axis at which function has the lowest output…

Q: 3. If f(x) = 2x² + 3x find f'(a) by using definition of derivative at a point a=4

A:

Q: Use the second derivative   f''(x)=x(x−1)(x−3)^2 to determine where the inflection points of f(x)…

A:

Q: What is the derivative of the attached function for x= -8   -1 -1/2 1 2

A: