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QJEEM22Ma08da: JEE Main 2022 Mathematics - Class 12 JEEM22Ma08da Solution: If denotes the greatest integer , then the number of points, at …

If [t][t] denotes the greatest integer ≤t\leq t , then the number of points, at which the function f(x)=4∣2x+3∣+9[x+12]−12[x+20]f(x)=4|2 x+3|+9\left[x+\frac{1}{2}\right]-12[x+20] is not differentiable in the open interval (−20,20)(-20,20) , is __________.

Step-by-Step Verified Solution

f(x)=4∣2x+3∣+9[x+12]−12[x+20]f(x)=4|2 x+3|+9\left[x+\frac{1}{2}\right]-12[x+20]

=4∣2x+3∣+9[x+12]−12[x]−240=4|2 x+3|+9\left[x+\frac{1}{2}\right]-12[x]-240

f(x)f(x) is non differentiable at x=−32x=-\frac{3}{2}

and f(x)f(x) is discontinuous at {−19,−18,….,18,19}\{-19,-18, \ldots ., 18,19\}

as well as {−392,−372,…,−32,−12,12,…,392}\left\{-\frac{39}{2},-\frac{37}{2}, \ldots,-\frac{3}{2},-\frac{1}{2}, \frac{1}{2}, \ldots, \frac{39}{2}\right\} ,

at same point they are also non differentiable

∴amp; Total number of points of non differentiability amp;=39+40amp;=79\begin{aligned}\therefore & \text { Total number of points of non differentiability } \\&=39+40 \\&=79\end{aligned}

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