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

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 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?

Consider the function f(x)={{:(x^(2)-5,xle3),(sqrt(x+13),xgt3):} Consider the following statements : 1. The function is discontinuous at x=3. 2. The function is not differentiable at x=0. What of the above statements is/are correct?

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 continuos at x=0. 2. The function f(x) is continuous at x=(pi)/(2) . Which of the above statements is/are correct?

A function f:RtoR is defined as f(x)=x^(2)" for "xge0,f(x)=-x" for "xlt0 . Consider the following statements in respect of the above function : 1. The function is continuous at x=0. 2. The function is differentiable at x=0. Which of the above statements is /are correct ?

Read the following information carefully and answer the question given below: Consider the function f(x)={{:(x^(2)-5,xle3),(sqrt(x+13),xgt3):} Consider the following statements: I. The function is discontinuous at x = 3 II. The function is not differentiable at x = 0 Which of the above statement(s) is/are correct?

The function f(x)=(x)/(1+|x|) is differentiable in:

Let f(x) be a function defined in 1lexltoo by. f(x)={:[(2-x,"for "1lexle2),(3x-x^(2),"for "xgt2):} Consider the function statements: I. The function is continuous every point in the interval [1,oo) II. The function is differentiable at x=15 . Which of the above statements is/are correct?

Consider the following statements : 1. The function f(x)=sinx decreases on the interval (0,pi//2) . 2. The function f(x)=cosx increases on the interval (0,pi//2) . Which of the above statements is/are correct ?