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

Option: 1

79


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\begin{aligned} & \mathrm{4|2 x+3|} \text{ is non-differentiable at } \mathrm{x=-\frac{3}{2}}\\ &\mathrm{9\left[x+\frac{1}{2}\right]} \text{ is non-differentiable at } \mathrm{\left.x+\frac{1}{2}\right]} \text { is } \\ & \mathrm{x=-19.5,-18.5, \ldots,-0.5,0.5, \ldots \quad \ldots, 19.5}\\ &\mathrm{-12[x+20]=-12[x]-240}\text{ is nondifferentiable at } \mathrm{x=-19,-18, \ldots, 0,1,2.}\\ &\therefore \text { Total }\mathrm{=40+39+1-1 }(\text { for } \mathrm{x=-\frac{-3}{2}}\text{ is common })\\ &\mathrm{=79}\\ &\text{Ans: 79} \end{aligned}

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