Question

Use the graph to state the absolute and local maximum and minimum values of the function. (Assume each point lies on the gridlines. Enter your answers as acomma-separated list. If an answer does not exist, enter DNE.)

find the absolute min and max values

find the local min and max values

((Textbook endchapter problem/ ch4.1 problem 5))

Answer 1

PART(a):

The local minimum/local maximum values exist at the points where the slope of the tangent is zero(i.e. horizontal tangent).

A local minimum is a point where the function is transitioning from decreasing to increasing.

From the graph, there is a local minimum at x = 2

floca Min = 2

A local maximum is a point where the function is transitioning from increasing to decreasing.

From the graph, there is a local maximum at x = 4

floca Mar = 5

PART(b):

The absolute maximum exists at x = 4 where there is horizontal tangent and the curve value is maximum at that point.

AbsMar = 5

The absolute minimum doesn't exist because the curve is minimum at x = 7 but it is undefined there.

Abs Min = DNE

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