Which of the following is true about point of extremum `x=a` of function `y=f(x)?` At `x=a ,` function `y=f(x)` may be discontinuous. At `x=a ,` function `y=f(x)` may be continuous but non-differentiable. At `x=a` ,function `y=f(x)` may have point of inflection. none of these

Options

A. At x =a, function y = f(x) may be discontinous
B. At x =a function y = f(x) may be continous but non differentiable
C. At x =a function y= f(x) may have point of inflection
D. none of these

Answer

1,2,3

Explanation

The following function is discontinous at x =2 but has point of maxima

f(x)=|x| has point of minima at x=0 thought it is non differetiable at x=0

In the following figure y=f(x) has point of inflection at x=0 as curve changed its concavity at x=0 howere x=0 is point of minima for the fucntion