Let f:(-2, 2) R be defined by f(x) = [x^2] |x^2 - 1| , where [t] denotes the greatest integer less than or equal to t . The number of points in the interval (-2, 2) where f is not differentiable is :

Step-by-step solution

Given f(x) = [x^2] |x^2 - 1| for x (-2, 2) . The possible points of non-differentiability are where the expression inside the greatest integer function is an integer, or where the expression inside the modulus is zero. In (-2, 2) , x^2 [0, 4) . The doubtful points are roots of x^2 = 0, 1, 2, 3 , which gives x = 0, 1, 2 , 3 . Let us examine continuity and differentiability at these points: At x = 2 and x = 3 : The function [x^2] has a jump discontinuity at these points. The value of |x^2 - 1| at x = 2 is 1 0 , and a