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Let f : R → R be define as : f(x) = {(a − b cos 2x)/x^2 ; x < 0 {x^2 + cx + 2 ; 0 ≤ x ≤ 1 {2x + 1 ; x > 1 If f is continuous every where in R and m is the number of points where f is NOT differential then m + a + b + c equal :

1. 4
2. 2
3. 1
4. 3

Correct answer: 2

Solution

The function f is continuous everywhere, which means the limits from both sides at the points where the piecewise definitions change must match. The points of potential non-differentiability occur at the boundaries of the intervals, specifically at x = 0 and x = 1. Since the function is continuous at these points but may not be smooth, there are two points where f is not differentiable, leading to m = 2.

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