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+1 vote
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in Continuity and Differentiability by (28.7k points)
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Rolle’s theorem is applicable in case of ϕ (x) = asinx , a > 0 in

A. Any interval

B. The interval [0, π]

C. The interval (0, π/2)

D. None of these

1 Answer

+1 vote
by (29.1k points)
selected by
 
Best answer

Correct answer is B.

Φ(x) = a Sin x , a > 0

Differentiating the above-mentioned function, with respect to ‘x’,

Φ’(x) = log a (cos x a Sin x)

\(\therefore\) Φ’(c) = log a (cos c a Sin c)

Let Φ’(c) = 0

log a (cos c a Sin c) = 0

cos c a Sin c = 0

cos c = 0

Also, the above-mentioned function, is derivable and continuous on the interval [0, π].

Thus, here Rolle’s Theorem is applicable on the above mentioned function in the interval [0, π].

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