JEE Main 2020 (Online) 6th September Evening ShiftQuestion 1
Let $f:\mathbf{R}\to\mathbf{R}$ be a function defined by $f(x)=\max\{x,x^2\}$. Let $S$ denote the set of all points in $\mathbf{R}$, where $f$ is not differentiable. Then :
Differentiation and its Application
Solution
Concept. $x$ and $x^2$ cross at $0$ and $1$; at each crossing the slopes differ. Formulas used. (1) $x^2\ge x\iff x\le0$ or $x\ge1$Step 1 - Pieces. By (1): $f=x^2$ for $x<0$, $f=x$ on $[0,1]$, $f=x^2$ for $x>1$. Step 2 - Slopes. At $0$: $0$ and $1$. At $1$: $1$ and $2$. Both are corners. Answer: (B)