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+1 vote
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in Continuity and Differentiability by (29.1k points)
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If f(x) = esin x in [0, π], then c in Rolle’s theorem is

A. \(\frac{\pi}{6}\)

B. \(\frac{\pi}{4}\)

C. \(\frac{\pi}{2}\)

D. \(\frac{3\pi}{4}\)

1 Answer

+2 votes
by (28.7k points)
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Best answer

Correct answer is D.

As, f(x) = eSin x

Differentiating the function with respect to ‘x’,

f’(x) = ex Cos x + Sin x ex

\(\therefore\) f’(c) = ec Cos c + Sin c ec

As, ex Cos x is continuous and derivable in R.

\(\therefore\) it is contionous on [0, π] and derivable on (0, π).

f(0) = e0 Sin (0)

= 0

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