Find the local linear approximation of...

Question

f(x) = cos²7x + x at x = 0. Then, use the approximation to estimate cos²(3.5) + 0.5.

A) 0.5

B) 4.5

C) 1.5

D) 1

Answer 1

f(0) = 1; f'(x) = - 14cos7xsin7x + 1; f'(0) = 1;

L(x) = 1 + 1(x - 0) = x + 1;

x = 0.5; L(0.5) = 0.5 + 1 = 1.5

f(0.5) = cos²3.5 + 0.5 ≈ L(0.5) = 1.5

Answer: C)