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

Let f(x) ={{:( ( 2x-1) "," ,"when" , x ge 1),( x",", "when", 0 le x le 1):} Show that f(x) is continuous but not differentiable at x =1

If f(x)={ax^(2)+b,x 1;b!=0, then f(x) is continuous and differentiable at x=1 if

If f(x) = {sinx , x lt 0 and cosx-|x-1| , x leq 0 then g(x) = f(|x|) is non-differentiable for

Let f(x) = int_(-2)^(x)|t + 1|dt , then a. f(x) is continuous in [-1, 1] b. f(x) is differentiable in [-1, 1] c. f'(x) is continuous in [-1, 1] d. f'(x) is differentiable in [-1, 1]

If f(x)={(1-cosx)/(xsinx),x!=0 and 1/2,x=0 then at x=0,f(x) is (a)continuous and differentiable (b)differentiable but not continuous (c)continuous but not differentiable (d)neither continuous nor differentiable

If f(x)={(1-cosx)/(xsinx),x!=0 and 1/2,x=0 then at x=0,f(x) is (a)continuous and differentiable (b)differentiable but not continuous (c)continuous but not differentiable (d)neither continuous nor differentiable

Show that f(x) = {:{(|2x-3|[x],xge1),(sin((pix)/(2)), x <1):} is continuous but not differentiable at x =1.

If f(x)= {|x|-|x-1|}^2 , draw the graph of f(x) and discuss its continuity and differentiability of f(x)

The function f(x) = |x| + |x-1| + |x-2| is continuous but not differentiable at for all x in R x=-1 and x=1

If f(x)={'x^2(sgn[x])+{x},0 Option 1. f(x) is differentiable at x = 1 Option 2. f(x) is continuous but non-differentiable at x = 1 Option 3. f(x) is non-differentiable at x = 2 Option 4. f(x) is discontinuous at x = 2