CBSE

MATHEMATICS · Multi correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

If f(x)={3x2+12x−1,−1≤x≤237−x,2<x≤3f(x)=\begin{cases}3x^2+12x-1, & -1\le x\le2\\37-x, & 2<x\le3\end{cases}, then (1) f(x)f(x) is increasing on [−1,2][-1,2] (2) f(x)f(x) is continuous on [−1,3][-1,3] (3) f′(x)f'(x) does not exist at x=2x=2 (4) f(x)f(x) has the maximum value at x=2x=2

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