The value of C in Rolle’s theorem for the function f(x) = e^xsin x ,…

The correct answer is Option (4) → \(\displaystyle\frac{3\pi}{4}\)

f is continuous on \([0, \pi]\) and differentiable on \((0, \pi)\), and

    \(f(0) = e^{0}\sin 0 = 0\)
    \(f(\pi) = e^{\pi}\sin\pi = 0\)

So Rolle’s theorem applies: there is a C in \((0, \pi)\) with \(f'(C) = 0\).

    \(f'(x) = e^{x}\sin x + e^{x}\cos x = e^{x}(\sin x + \cos x)\)

Since \(e^{x} \ne 0\),

    \(\sin C + \cos C = 0\)
    \(\tan C = -1\)

In \((0, \pi)\) this gives

    \( \displaystyle C = \frac{3\pi}{4} \)

Note: This topic was not in the CUET 2026 syllabus.