Answer :
Final answer:
The value of f−1'(99) is calculated as 1 / f'(66), which using the given information f'(66) = 77, would be 1/77. Since 1/77 is not among the options given, the correct answer is d) None of the above.
Explanation:
The value of f−1'(99) can be found using the derivative of the inverse function. Based on the property that if f is a one-to-one function with a derivative f' at a point a, and its inverse function f−1 has a derivative at point b = f(a), then:
f−1'(b) = 1 / f'(a)
Given that f(66) = 99 and f'(66) = 77, we substitute a with 66 and b with 99 to get:
f−1'(99) = 1 / f'(66) = 1 / 77
The value of f−1'(99) is therefore 1/77 and not any of the given options a) 66 b) 77 c) 99, which implies that the correct answer is d) None of the above.
