Question

Can Mean Value Theorem be applied in the curve

(a) =\(\begin{cases}3sin(x)&0<x<\pi/4 \\ sin(x)-cos(x)&\pi/4<x<\pi/2\end{cases}\)

(b) True

(c) False

The question was asked during an online exam.

Asked question is from Lagrange’s Mean Value Theorem in portion Differential Calculus of Engineering Mathematics

Answer 1

Correct answer is (b) True

The best I can explain: Continuity Check

\(\lim_{x\rightarrow π/4-}f(x) = 3Sin(\frac{π}{4}) = 3/\sqrt{2}\)

\(\lim_{x\rightarrow π/4+)}f(x) = Sin(π/4)- Cos(π/4) = 0\)

Since \(\lim_{x\rightarrowπ/4+} ≠ \lim_{x\rightarrowπ/4-}\)

Function f(x) is not continuous hence mean value theorem cannot be applied.