Question

Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
f(x) =

x2 if −1 ≤ x ≤ 0
7 − 9x if 0 < x ≤ 1

Answer 1

From the sketch, we can see the graph has a discontinuity at $x=0$ and $f(0)=0$ .

MInimas are:

Local Minima $=0$ and $-2$ at $x=0$ and $x=1$ respectively.

Gloabal Minima $f(x)=-2$ at $x=1$

Maximas are:

Local Maxima $=1$ at $x=-1$ only.

Global Maxima $=DNE$ ; this is because the function has a discontinuity at $x=0$ and the function does not attain the value of 7.