Suppose f is a one-to-one function with f(2)=8 and f’(2)=4. What is the value of (f^-1)’(8)?
1 answer:
Answer:
1/4
Step-by-step explanation:
The tangent line to f(x) at x=2 goes through the point (2, 8) and has slope 4.
The inverse function f⁻¹(x) is a reflection of the function f(x) across the line y=x. The corresponding tangent line will go through point (8, 2) and have slope 1/f'(2) = 1/4 at that point. That is, ...
(f⁻¹)'(8) = 1/f'(f⁻¹(8)) = 1/f'(2) = 1/4
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