STATEMENT 1: `int_0^x|sint|dt ,forx in [0,2pi],` is a non-differentiable function. STATEMENT 2: `|sint|` is non-differentiable at `x=pidot`

Which of the function is non-differential at x=0?f(x)=x|x|

Which of the function is non-differential at x=0?f(x)=|x^(3)|

Which of the function is non-differential at x=0?f(x)=cos|x|

f(x)=int_0^x e^t f(t)dt+e^x , f(x) is a differentiable function on x in R then f(x)=

If f(x)= int_(0)^(x)(f(t))^(2) dt, f:R rarr R be differentiable function and f(g(x)) is differentiable at x=a , then

A function f(x) is defined as follows: f(x)={{:(x+pi," for ",x""in[-pi","0)),(picosx," for ",x""in[0","(pi)/(2)]),((x-(pi)/(2))^(2)," for ",x""in((pi)/(2)","pi]):} Consider the following statements : 1. The function f(x) is differentiable at x=0. 2. The function f(x) is differentiable at x=(pi)/(2) . Which of the above statements is /aer correct ?

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 ?

Consider the following for the next two items that follows f(x)={{:(x+pi" for "x in[-pi.0)),(picosx" for "x in[0.(pi)/(2)]),((x-(pi)/(2))^(2)" for "x in((pi)/(2).pi]):} Consider the following statement: 1. The function f(x) is differentiable at x = 0. 2. The function f(x) is differentiable at x=(pi)/(2) Which of the above statements is / are correct?

If g(x)=int_(0)^(x)2|t|dt, then (a)g(x)=x|x|(b)g(x) is monotonic (c) g(x) is differentiable at x=0(d)g'(x) is differentiable at x=0