Same chapter3 marksDifficulty: Medium
Differentiate y = sin(x2) with respect to x.
Continuity and Differentiability
3 marksDifficulty: Medium
State Rolle's theorem and Lagrange's mean value theorem.
Original Khojo Papers practice question — not from a past board paper.
Answer
Rolle's theorem states that if f is continuous on [a, b], differentiable on (a, b) and f(a) = f(b), then there is at least one c in (a, b) with f′(c) = 0. Lagrange's mean value theorem drops the condition f(a) = f(b) and concludes that there is a c with f′(c) = [f(b) − f(a)]/(b − a).
No citable source has been recorded for this record. Treat it as practice material, not as fact.
Explanation
Rolle's theorem is the special case of Lagrange's in which the chord is horizontal.
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