The value of c in Rolle’s Theorem

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Continuity and Differentiability

Question:

The value of c in Rolle’s Theorem for the function f (x) = e^x sinx, x∈ [π 0, ] is :

Options:

π/6

π/4

2π/3

3π/4

Correct Answer:

3π/4

Explanation:

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