Approximate the critical numbers of the function shown in the graph.

Question

Determine whether the function has a relative maximum, a relative minimum, an absolute maximum, an absolute minimum, or none of these at each critical number on the interval shown. (Enter your answers as a comma-separated list.)

https://www.webassign.net/waplots/4/c/04761a74ddfa6ec2ed5e96a80f8598.gif

Approximate the critical numbers.

x =

List the critical numbers at which each phenomenon occurs. (If an answer does not exist, enter DNE.)

relative maxima =

relative minima =

absolute maxima =

absolute minima =

Answer 1

The critical numbers make the derivative 0. Visually, this looks like a horizontal tangent. Inspecting the graph, we see this occurs at (1,1) and (3,1). These points also appear to be our relative maxima. It appears that the graph is discontinuous at (0,0) and (4,0), so the absolute minimum is (2,0)