Differentiability at a Point

Investigate the function y = |cosx| for differentiability at the points x=(pi)/(2)+npi (n an integer).

Examine for continuity and differentiability the points x=1 and x=2, the function f defined by f(x)=[{:(X[X],",",0leX where[X]=greatest integer less than or equal to x.

Give an example of a function which is continuous but not differentiable at a point.

If a function is differentiable at a point,it is necessarily continuous at that point.But; the converse is not necessarily true.

Define differentiability of a function at a point.

Show that f(x)={[5-x,,x>=2],[x+1,,x<2] is continuous at x = 2 but not differentiable at that point.

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)={{:(,(1)/(|x|),"for "|x| gt1),(,ax^(2)+b,"for "|x| lt 1):} If f(x) is continuous and differentiable at any point, then

Consider the following statements: 1. The derivative where the function attains maxima or minima be zero. 2. If a function is differentiable at a point, then it must be continuous at that point. Which of the above statements is/are correct ?