QJEEM24Ma488f: JEE Main 2024 Mathematics - Class 12 JEEM24Ma488f Solution: Let . If and denote the number of points where is not…

Question

Verified Solution • 2025–26 Session moderate

Let

f(x)=\left|2 x^2+5\right| x|-3|, x \in \mathbf{R}

. If

\mathrm{m}

and

\mathrm{n}

denote the number of points where

f

is not continuous and not differentiable respectively, then

\mathrm{m}+\mathrm{n}

is equal to :

Accepted Answer

\begin{aligned} &amp; f(x)=\left|2 x^2+5\right| x|-3| \\\\ &amp; \text { Graph of } y=\left|2 x^2+5 x-3\right|\end{aligned}

Now

f(x)

is continuous

\forall x \in R

but non- differentiable at

x=\frac{-1}{2}, \frac{1}{2}, 0

\begin{aligned}\therefore m &amp; =0 \\\\n &amp; =3 \\\\m+n &amp; =3\end{aligned}

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