Is every continuous function differentiable?

The function f(x)=|cosx| is (a) everywhere continuous and differentiable (b) everywhere continuous but not differentiable at (2n+1)pi//2 , n in Z (c) neither continuous nor differentiable at (2n+1)pi//2 , n in Z (d) none of these

Show that the function f(x)={x^msin(1/x),\ \ \ x!=0 0,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=0 is neither continuous nor differentiable, if mlt=0

If f(x)=|(log)_e|x|| , then (a) f(x) is continuous and differentiable for all x in its domain] (b) f(x) is continuous for all x in its domain but not differentiable at x=+-1 (c) f(x) is neither continuous nor differentiable at x=+-1 (d) none of these

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

Write an example of a function which is everywhere continuous but fails to be differentiable exactly at five points.

Write an example of a function which is everywhere continuous but fails to be differentiable exactly at five points.

f(x) ={{:(1-sqrt(1-x^(2)),if -1lexle1),(1+ log ""(1)/(x), if xgt1):} (a) continuous and differentiable at x=1 (b) continuous but not differentiable at x=1 (c) neither continuous nor differentiable at x=1 (d) none of these

Which of the following function is continuous everywhere but not differentiable at atleat one point in its domain

Does there exist a function which is continuous everywhere but not differentiable at exactly two points? Justify your answer.