The mean value theorem states that if is a continuous function on and is differentiable in ( and being any two real numbers), then there exists at least one real number such that .
Suppose , and . Which of the following can be taken as a value of ?
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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) = x², a = 3 and b = 6. Which of the following can be taken as a value of c? (A) 4·4 (B) 4·6 (C) 4·8 (D) None of the above
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^2, a = 3 and b = 6. Which of the following can be taken as a value of c?
Limits, continuity and differentiability has come up 122 times in 7 exams since 2006.
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.
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Question from the JNU SSS 2014 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.