Mathematics

Problem

Answer the following questions related to critical points of a real-valued function. a. (i) Define a point of local maximum and a point of local minimum of a function

f:\mathbb R\to\mathbb R

. b. (ii) For the function

f(x)=|x-3|

, show that

f

is continuous but not differentiable at

x=3

. c. (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.

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