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Show that the linearization of f(x) = (1+x)k at x = 0 is L(x) = 1 + kx.

Show that the linearization of f(x) = (1+x)k at x = 0 is L(x) = 1 + kx.

Calculus For The Life Sciences
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.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 35E
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K Show that the linearization of f(x) = (1+x)k at x = 0 is L(x) = 1 + kx. O 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). O A. f'(x) = (1+x)k OB. f'(x)=k(1+x)k-1 OC. f'(x)=(1+x)k-1 OD. f'(x)=k(1+x)k 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. ) = f(0) + f'(0)(x 0+k(x-0) = 1+kx O B. 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)=k+1(x-0) = 1+kx
Transcribed Image Text:K Show that the linearization of f(x) = (1+x)k at x = 0 is L(x) = 1 + kx. O 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). O A. f'(x) = (1+x)k OB. f'(x)=k(1+x)k-1 OC. f'(x)=(1+x)k-1 OD. f'(x)=k(1+x)k 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. ) = f(0) + f'(0)(x 0+k(x-0) = 1+kx O B. 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)=k+1(x-0) = 1+kx
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