Thread: Inverse Derivative

For f(x) = 2x^5 + 3x^3 + x

Find (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?

Thanks.

As soon as you're given f(x), you can find its derivative . You also need to find the inverse of f evaluated at 6: by inspection.

Now you just plug that information into your equation to get the answer.

Can you please show how you got f^-1(6) = 1

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:



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