Question

or ƒ(x) = (x – 1)^2/3, the mean value theorem is applicable to ƒ(x) in the interval –

• A. [2, 4]
• B. [0, 2]
• C. [–2, 2]
• D. Any finite interval

Answer 1

Answer: (A)

$2, 4$

Answer 2

Since ƒ ′ (x) does not exist at x = 1, (Q ƒ ′ (x) = $\frac{2}{3}$ (x – 1)^–1/3) therefore, mean value theorem is not applicable to the given function in any interval which contains 1 as an interior point. So, in this case the required interval is [2, 4].