f(x) = x3+ x. Note that f(2) = 10. Find (f-1)`(10).
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= y3 + y
- Differentiate implicitly 1= (3y2 + 1)y`
- Solve for y`. y`= 1 / (3y2 + 1). Since y = f-1, then y` = (f-1)`
Therefore (f-1)` = 1 / (3y2 + 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!