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Questions › JNU › JNU SSS 2014 › Q60
2 marks, −0.5Mathematics › Limits, continuity and differentiability › Mean value theorem and Rolle's theoremModerateabout 2 min

JNU SSS 2014 Question 60: Limits, continuity and differentiability

The mean value theorem states that if fff is a continuous function on [a, b][a,\ b][a, b] and is differentiable in (a, b)(a,\ b)(a, b) (aaa and bbb being any two real numbers), then there exists at least one real number c∈(a, b)c \in (a,\ b)c∈(a, b) such that f(b)−f(a)=f′(c)(b−a)f(b) - f(a) = f'(c)(b - a)f(b)−f(a)=f′(c)(b−a).

Suppose f(x)=x3f(x) = x^3f(x)=x3, a=−1a = -1a=−1 and b=2b = 2b=2. How many value(s) of ccc is/are possible?

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The mean value theorem states that if f is a continuous function on [a, b] and is differentiable in (a, b) (a and b being any two real numbers), then there exists at least one real number c ∈ (a, b) such that f(b) - f(a) = f′(c)(b - a). Suppose f(x) = x³, a = -1 and b = 2. How many value(s) of c is/are possible? (A) None (B) One (C) Two (D) Three

Also written as: The mean value theorem states that if f is a continuous function on [a, b] and is differentiable in (a, b) (a and b being any two real numbers), then there exists at least one real number c in (a, b) such that f(b) - f(a) = f'(c)(b - a). Suppose f(x) = x^3, a = -1 and b = 2. How many value(s) of c is/are possible?

Limits, continuity and differentiability has come up 122 times in 7 exams since 2006.

What this question tests

This question is on Mean value theorem and Rolle's theorem, part of Limits, continuity and differentiability in Mathematics.

Results linking the average rate of change to a derivative at some point.

TestStop has 13 past-paper questions on this subtopic.

Practise Limits, continuity and differentiabilityMore on Mean value theorem and Rolle's theorem

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