Statement 1: `f(x)=|x-1|+|x-2|+|x-3|` has point of minima at `x=3.` Statement 2: `f(x)` is non-differentiable at `x=3.`

If f(x)=|x|+|x-1|-|x-2|, then-(A) f(x) has minima at x=1

If f(x)={x^(3),x^(2) =1 then f(x) is differentiable at

Consider the following statements: 1. The function f(x)=|x| is not differentiable at x=1. 2. The function f(x)=e^(x) is not differentiable at x=0. Which of the above statements is/are correct ?

Statement I :The function f(x)=(x^(3)+3x-4)(x^(2)+4x-5) has local extremum at x=1. Statement II :f(x) is continuos and differentiable and f'(1)=0.

Consider the following statements in respect of f(x)=|x|-1 : 1. f(x) is continuous at x=1. 2. f(x) is differentiable at x=0. Which of the above statement is/are correct?

STATEMENT-1: f(x)=|x-1|+|x+2|+|x-3| has a local minima . and STATEMENT-2 : Any differentiable function f(x) may have a local maxima or minima if f'(x)=0 at some points where f'(x)=0.

If f(x) = [[x^(3),|x| =1] , then number of points where f(x) is non-differentiable is