The value of c in Rolle’s Theorem for the function f (x) = e x sinx, x∈ [π 0, ] is :
Answer & explanation
Correct answer: option 4
By Rolle's Theorem : f'(c) = 0;
f'(x) = e x Sin x + e x Cos x
f'(x)|x=c = e x Sin x|x=c + e x Cos x|x=c
0 = e x or 0 = (Sin x + Cos x)
x = 1, 3π/4