Answer the following questions related to critical points of a real-valued function.
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
Answer the following questions related to critical points of a real-valued function.
(i) Define a point of local maximum and a point of local minimum of a function f:R→R.
(ii) For the function f(x)=∣x−3∣, show that f is continuous but not differentiable at x=3.
(iii) By examining the behaviour of f on intervals immediately to the left and right of x=3, decide whether x=3 gives a local maximum, a local minimum or neither. Justify your answer.