Sketch the graph of f and use your sketch to find the absolute and local maximum and minimum values of f.

Question

Sketch the graph of f 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) = x^2 if -1 ≤ x ≤ 0

f(x) = 3 - 7x if 0 < x ≤ 1

Find the absolute minimum value and local maximum value(s).

Answer 1

Hello, Sofia,

I plotted both functions and colored their ranges. The graph won't fit here, however. Try it yourself if you are having a hard time visualizing the lines.

Maximum y occurs at (0,3) for the y=3-7x line at the left of it's range

Maximum y for y = x² occurs at (-1,1)

Minimum y for y=3-7x occurs at ( 1,-4)

Minimum y for y = x² occurs at (-1,1)

I'm a little uncertain to the "absolute value," but if it means the absolute value of y, the point (1,-4) becomes the maximum at (1,4)

Bob