If [t] denotes the greatest integer ≤ t, then the number of points, at which the function f(x)=4|2 x+3|+9[x+1/2]-12[x+20] is not differentiable in the open interval (-20,20), is _ _ _ _ _.

Limit, Continuity and Differentiability: JEE Main 2022 Mathematics question

JEE Main 2022 · 29 Jul, Evening shift · Q35

JEE Main 202229 Jul, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

[t]

denotes the greatest integer

\leq t

, then the number of points, at which the function

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)

, is __________.

Your answerType your answer. Integers and decimals are accepted.