Question

What is the relation between f(a) and f(h) according to another form of Rolle’s theorem?

(a) f(a) < f(a+h)

(b) f(a) = f(a+h)

(c) f(a) = f(a-h)

(d) f(a) > f(a+h)

The question was posed to me in an online quiz.

The doubt is from Mean Value Theorem topic in division Continuity and Differentiability of Mathematics – Class 12

Answer 1

The correct choice is (b) f(a) = f(a+h)

Easy explanation: According to Rolle’s theorem, if f : [a,a+h] → R is a function such that

i) f is continuous on [a,a+h]

ii) f is differentiable on (a,a+h)

iii) f(a) = f(a+h) then there exists at least one θ c ∈ (0,1) such that f’(a+θh) = 0