JEE Main 2025 Apr 4 Shift 1, Mathematics Q25: Differentiability Of A Function

JEE Main2025Apr 4, Shift 1Mathematics

Let $m$ and $n$ be the number of points at which the function $f (x) = max {x, x^{3}, x^{5}, \dots, x^{21}}$ , $x \in R$ , is not differentiable and not continuous, respectively. Then $m + n$ is equal to _____.

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Solution

$f(x)= \begin{cases} x, & x<-1\\[2mm] x^{21}, & -1\le x<0\\[2mm] x, & 0\le x<1\\[2mm] x^{21}, & x\ge1 \end{cases}$

$f (x)$ is continuous everywhere.

$∴ n = 0$

$f'(x)= \begin{cases} 1, & x<-1\\[2mm] 21x^{20}, & -1 \le x < 0\\[2mm] 1, & 0 \le x< 1\\[2mm] 21x^{20}, & x \ge 1 \end{cases}$

$f (x)$ is non-differentiable at $x = - 1, 0, 1$ .

$∴ m = 3$

$m + n = 3$

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JEE Main 2025 Apr 4 Shift 1, Mathematics Q25: Differentiability Of A Function

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