KShow that the linearization of f(x) = (1+x)k at x=0 is L(x) = 1 + kx.If f is differentiable x = a at then the approximating function L(x) = f(a) + f'(a)(x-a) is the linearization of f at a. Determine f(0).f(0) = (Simplify your answer.)Determine f'(x).OA. f'(x)= (1+x)kOB. f'(x)=k(1+x)kO c. f'(x) = (1+x)k-1OD. f'(x)=k(1+x)k-1Determine f'(0).f'(0) =Using the values of f(0) and f'(0) found in the previous steps, determine the linearization L(x) = f(a) + f'(a)(x-a) for a = 0.OA. L(x)=f(0) + f'(0)(x-0)=k+1(x-0) = 1+kxOB. L(x)=f(0) + f'(0)(x - 0) = 1 +k(x-0)=1+kxOC. L(x)=f(0) + f'(0)(x-0) = 1 +x+k(0) = 1+kxOD. L(x)=f(0) + f'(0)(x- 0) = 0+k(x-0) = 1+kx

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Show that the linearization of f(x) = (1+x)k at x=0 is L(x) = 1+kx. If f is differentiable x = a at then the approxim

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.CR: Chapter 3 Review

Problem 12CR: Determine whether each of the following statements is true or false and explain why. The derivative...

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Question

K
Show that the linearization of f(x) = (1+x)k at x=0 is L(x) = 1 + kx.
If f is differentiable x = a at then the approximating function L(x) = f(a) + f'(a)(x-a) is the linearization of f at a. Determine f(0).
f(0) = (Simplify your answer.)
Determine f'(x).
OA. f'(x)= (1+x)k
OB. f'(x)=k(1+x)k
O c. f'(x) = (1+x)k-1
OD. f'(x)=k(1+x)k-1
Determine f'(0).
f'(0) =
Using the values of f(0) and f'(0) found in the previous steps, determine the linearization L(x) = f(a) + f'(a)(x-a) for a = 0.
OA. L(x)=f(0) + f'(0)(x-0)=k+1(x-0) = 1+kx
OB. L(x)=f(0) + f'(0)(x - 0) = 1 +k(x-0)=1+kx
OC. L(x)=f(0) + f'(0)(x-0) = 1 +x+k(0) = 1+kx
OD. L(x)=f(0) + f'(0)(x- 0) = 0+k(x-0) = 1+kx

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