Find the linear approximation, L(x), to f(x) at x = x₀. f(x) = e⁷^x, x₀ = 0 A) L(x) = 7x B) L(x) = -7x + 1 C) L(x) = 7ex - 1 D) L(x) = 7x + 1

Question

Quizplus · Accepted Answer

To use linear approximation, we need to find the first derivative of f(x):

f'(x) = e^(-x)

Then, the linear approximation can be written as:

L(x) = f(10) + f'(10)(x-10)

Now, we can substitute the values given in the problem:

f(10) = e^(17) + 0 = e^(17)

f'(10) = e^(-10)

L(x) = e^(17) + e^(-10)(x-10)

Simplify and rewrite in the desired format:

L(x) = 7x + 1

Therefore, the best choice is D.

Find the Linear Approximation, L(x), to F(x) at X =