AP Calculus ABmediummcq1 pt
The derivative of the inverse function f⁻¹ at a point can be found using:
A.(f⁻¹)'(b) = 1/b
B.(f⁻¹)'(b) = -f'(b)
C.(f⁻¹)'(b) = 1/f'(f⁻¹(b))
D.(f⁻¹)'(b) = f'(b)
Explanation
Core Concept
The derivative of the inverse function formula: (f⁻¹)'(b) = 1/f'(a) where a = f⁻¹(b). This follows from differentiating the identity f(f⁻¹(x)) = x using the chain rule.
Correct Answer
C(f⁻¹)'(b) = 1/f'(f⁻¹(b))
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