Let `f (x) = max {1-x, 1 + x, 2}`. Prove that `f (x)` is continuous at all points but notdifferentiable at `x = 1 and x =-1`.

Let f(x) be a real valued function such that f(a)=0. If g(x)=(x-a)f(x) is continuous but notdifferentiable at x=a and h(x)=(x-a)^(2)f(x) is continuous and differentiable at x=a .Then f(x)

Let f(x) = {{:(min{x, x^(2)}, x >= 0),(max{2x, x^(2)-1}, x (A) f(x) is continuous at x=0 (B) f(x) is differentiable at x=1 (C) f(x) is not differentiable at exactly three point (D) f(x) is every where continuous

Let f(x) = {:{(x+a, x le1),(ax^2 + 1, x > 1):} . Show that f is continuous at 1. Find 'a' so that it is derivable at 1.

Let f(x)={x+1 if x 1 for what a will the function f(x) be continuous?

Let f(x) = {:(1/(x^2) , : |x| ge 1),(alphax^2 + beta , : |x| < 1):} . If f(x) is continuous and differentiable at any point, then

Let f(x)= {:{((x+a) , x lt1),( ax^(2)+1, xge1):} then f(x) is continuous at x =1 for

Let f(x)=sin^(-1)((2x)/(1+x^(2)))AA x in R. The function f(x) is continuous everywhere but not differentiable at x is/ are

If f(x)=2x+|x-x^(2)|,-1<=x<=1 ,then f(x) is is(a) continuous but not differentiable in [-1,1]

Let f(x)=ax+1,x For what values of a and b is f(x) continuous at x=1