The value of c in Mean value theorem for

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Continuity and Differentiability

Question:

The value of c in Mean value theorem for the function f (x) = x (x – 2), x ∈ [1, 2] is :

Options:

3/2

2/3

1/2

5/3

Correct Answer:

3/2

Explanation:

By Mean Value Theorem : f'(x)|_x=c = [f(b) - f(a)] / [b-a]

f'(x) = 2x-2

f'(x)|_x=c = 2x-2|_x=c= 2c-2

[f(b) - f(a)] / [b-a] = [0 + 1] / 1 = 1

2c-2 = 1

c = 3/2