The number of points, at which the function f(x) =, 2x + 1, - 3| x + 2, +, x2 + x - 2 |, x\[\in\]R is not differentiable, is \_\_\_\_\_\_\_\_\_\_.
Answer: 2
Solutions · 1
Official solution
x2+x−2=(x+2)(x−1). Critical points are x=−21,−2,1. Writing f piecewise on each interval and comparing f′ at the joins:
At x=1: left/right derivatives −2×1−2=−4 and 2×1=2 --- not equal, non-differentiable.
At x=−2: both sides give −2 --- differentiable.
At x=−21: left/right derivatives −5 and −1 --- not equal, non-differentiable.
So f is non-differentiable at exactly 2 points (x=1,−21).