Let f be differentiable and invertible, with f(3) = 7 and f'(3) = 5. What is (f⁻¹)'(7)?
Correct answer: B. 1/5
- A. 5
- B. 1/5
- C. 3/7
- D. 7/3
Explanation
The derivative of an inverse function is (f⁻¹)'(y) = 1/f'(f⁻¹(y)). Since f⁻¹(7) = 3 and f'(3) = 5, the value is 1/5.
Report an error
The more specific you are, the faster it gets fixed. A source beats an opinion.
Prefer email? support@testustad.com
Practise Differentiation and Optimisation
30 free Differentiation and Optimisation MCQs from Quantitative Methods, each with the correct answer and an explanation. Unlimited attempts, no account needed.
Exams that ask Quantitative Methods questions like this
Quantitative Methods is on this paper prepared for on TestUstad, and all of them draw the same bank, so this question is worth knowing for it.
More Differentiation and Optimisation questions
The marginal cost of producing q units is MC(q) = 2q + 10, and the marginal revenue is MR(q) = 50 - 2q. At what positive output is profit stationary?
A differentiable function satisfies f(2) = 5 and f(6) = 17. What value must f'(c) have for at least one c between 2 and 6?
For f(x) = x⁴ - 4x², which statement about x = 0 is correct?
Two positive numbers have sum 20. What is the maximum possible value of their product?
For the curve y = x³ - 2x + 1, what is the equation of the normal at x = 1?
A spherical balloon is inflated so that its radius increases at 2 cm per second. At the instant its radius is 3 cm, how fast is its volume increasing?