Define the function by .

MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Define the function

g:\mathbb{R}\to\mathbb{R}

g(x)=|x^{2}-4x|+3

. (i) Rewrite

g(x)

without the absolute value sign by specifying suitable intervals of

x

." (ii) For each interval obtained in (i), find all stationary points of

g

within that interval." (iii) Classify every stationary point obtained in (ii)." (iv) Using the values of

g

at stationary points and any end–points of the relevant intervals, determine the least value of

g

and hence write the range of

g

(-\infty,\infty)