Continuity And Differentiability Question 2
Question 2 - 2024 (01 Feb Shift 2)
Let $f(\mathrm{x})=\left|2 \mathrm{x}^{2}+5\right| \mathrm{x}|-3|, \mathrm{x} \in \mathrm{R}$. If $\mathrm{m}$ and $\mathrm{n}$ denote the number of points where $f$ is not continuous and not differentiable respectively, then $m+n$ is equal to :
(1) 5
(2) 2
(3) 0
(4) 3
Show Answer
Answer (4)
Solution
$f(x)=\left|2 x^{2}+5\right| x|-3|$
Graph of $y=12 x^{2}+5 x-3$
Number of points of discontinuity $=0=\mathrm{m}$
Number of points of non-differentiability $=3=n$
