JEE Main 2022 · 29 Jul · Shift 2 · Mathematics Q26

← JEE Main 2022 · 29 Jul · Shift 2

MathematicsInteger+4 / -1Question 26 of 90

If [t] denotes the greatest integer ≤ t, then the number of points, at which the function $f(x)=4|2x+3|+9\left[x+\dfrac12\right]-12[x+20]$ is not differentiable in the open interval (−20, 20), is _______.

Your answer

Answer and worked solution

Official answer: 79

Jumps. $[x+20]=[x]+20$ , so $f=4|2x+3|+9\left[x+\frac12\right]-12[x]-240$ . The first floor jumps at the 40 half-integers in (−20, 20), the second at the 39 integers; they never cancel. The corner of $|2x+3|$ at $-\frac32$ is one of the half-integers.

Total 79.

Answer: 79

Topics:Differentiability

← Previous question Next question →

JEE Main 2022 · 29 Jul · Shift 2, Mathematics question 26