Question

Let f and g be functions satisfying the following conditions:

(a) f(0) = 1, (b) f'(x) = g(x), g'(x) = f(x), (c) g(0) = 0.
Estimate f(1) to three decimal places

Answer 1

1

Explanation:

Linearization equation: L(x)=f(a)+f′(a)(x−a)

L(1) = f(0) + f'(0)(1-0)

L(1) = 1 + 0(1) =1

g(0) is equal to f'(0), so I substituted g(0) for f'(0) in the Linearization equation

This estimation is extremely off due to how big the change in x is.