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