JEE Main 2022 · 25 Jul · Shift 1 · Mathematics Q26

← JEE Main 2022 · 25 Jul · Shift 1

MathematicsInteger+4 / -1Question 26 of 90

Let $f(x)=\begin{cases}\left|4x^2-8x+5\right|, & \text{if }8x^2-6x+1\ge0\\ \left[4x^2-8x+5\right], & \text{if }8x^2-6x+1<0,\end{cases}$ where $[\alpha]$ denotes the greatest integer less than or equal to $\alpha$ . Then the number of points in $\mathbf R$ where $f$ is not differentiable is ______.

Your answer

Answer and worked solution

Official answer: 3

Shape. $4x^2-8x+5=4(x-1)^2+1>0$ is smooth. On $\left(\frac14,\frac12\right)$ the floor applies; there the quadratic falls from 3.25 to 2, crossing 3 at $x=1-\frac1{\sqrt2}$ .

Breaks at $\frac14$ , $1-\frac1{\sqrt2}$ (jumps) and $\frac12$ (slope 0 against $-4$ ): 3.

Answer: 3

Topics:Differentiability Graphs of functions

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JEE Main 2022 · 25 Jul · Shift 1, Mathematics question 26