- #1

jumbogala

- 423

- 4

## Homework Statement

f(x) = x

^{3}+ x. Note that f(2) = 10. Find (f

^{-1})`(10).

## Homework Equations

## The Attempt at a Solution

Note that where I have written ` it denotes prime (as in the derivative of).

- Switch the x and y variables. x= y

^{3}+ y

- Differentiate implicitly 1= (3y

^{2}+ 1)y`

- Solve for y`. y`= 1 / (3y

^{2}+ 1). Since y = f

^{-1}, then y` = (f

^{-1})`

Therefore (f

^{-1})` = 1 / (3y

^{2}+ 1)

Since f(2) = 10, f

^{-1}(10)=2. But my equation is(f

^{-1})`,

**not**just

f

^{-1}! I don't know what to do after this point!