For f(x) = 2x^5 + 3x^3 + x
Find (f^-1)' (6)
How do you do this?
The formula is d/dx (f^-1(x)) = 1/ (f'(f^-1(x))
How do I set it up?
To find , you need to find a value for x that makes y equal to 6. That is, you need to find the solution for .
Notice that the coefficients of f(x) add up to 6. Knowing this, all you have to do is plug in x=1 to make the x's "disappear":
A general way to solve this type of problem is to use synthetic division to factor the polynomial: