Mark the correct alternative in the following:
Rolle’s theorem is applicable in case of ϕ (x) = asinx, a > 0 in
Φ(x) = aSin x, a > 0
Differentiating the above-mentioned function, with respect to ‘x’,
Φ’(x) = log a (cos x a Sin x)
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].
Hence, Option (B) is the answer.