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.)

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) =	x2	if −1 ≤ x ≤ 0
8 − 9x	if 0 < x ≤ 1

absolute maximum value

 

absolute minimum value

 

local maximum value(s)

 

local minimum value(s)

Answer 1

Normally on a closed interval we would say there is a guaranteed absolute max/min, but that is only the case is the function is continuous on that interval. The described piecewise function has a jump discontinuity at x = 0. There is an absolute min at x = 1, but no ABSOLUTE max. The limit as x approaches zero from the right is 8. It looks like there should be a relative min at x = 0, but this would be one sided (as x approaches 0 from the left).

Check it out here to get the idea.

desmos.com/calculator/s59omaufc1