Question

Let y = [f(x)]3 and suppose that f′ (1) = 4 and y′ = 10 for x = 1. Find f(1)?

Answer 1

Below

Explanation:

Inputs:

`y = [f(x)]^3 qquad [= f^3]`

`implies y′ = 3 f^2 f'`

Given:

• `f′ (1) = 4 qquad triangle`

• `y′(1) = 10 qquad implies (3 f^2(1) f'(1) = 10 qquad square)`

Find `f(1)`:

`(triangle)/(square) implies ( f′ (1))/(3 f^2(1) f'(1)) = (4)/(10)`

`implies (1)/(3 f^2(1)) = (4)/(10)`