For each of the given function f(x), find the derivative (f^-1)' (c) at the given point c, first finding a = f^-1 (c).

Question

For each of the given functions f(x), find the derivative (f^-1)' (c) at the given point c, first finding a = f^-1(c).

1. f(x) = 4x +6x^15, c = -10 a = ?
2. (f^-1)' (c) = ?
3. f(x) = x^2 -13x + 52 on the interval [6.5, inf); c = 16 a = ?
4. (f^-1)(c) = ?

Answer 1

f(x) = 4x + 6x¹⁵

To find [f^-1(-10)]', we first must find the number a such that f(a) = -10. By trial and error, we see that f(-1) = -10.

Next, we need the value of f'(-1). Since f'(x) = 4 + 90x¹⁴, we have f'(-1) = 94.

Then [f^-1(-10)]' = 1/94.

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f(x) = x² - 13x + 52. It can be shown that f(9) = 16.

Find f'(9) and then take the reciprocal to get [f^-1(16)]'