Relative Maximum and Relative Minimum Lesson

Relative Maximum and Relative Minimum Lesson

Relative Maximum Definition

A relative maximum point is a point where the function changes direction from increasing to decreasing (making that point a "peak" in the curve). Can also be called "local maximimum".

Points Q and S

Relative Minimum Definition

A relative minimum point is a point where the function changes direction from decreasing to increasing (making that point a "bottom" in the curve). Can also be called "local minimum".

Points P, R, and T

Multiple Choice

Does the graph have a relative maximum or relative minimum?

• Maximum

• Minimum

Multiple Choice

What is the relative maximum?

• (1,2)

• (2,2)

• (0,-2)

Multiple Choice

What is the relative minimum?

• (1,2)

• (2,2)

• (0,-2)

Multiple Select

Identify all local minimums.

•  $\left(3.25,\ 2.25\right)$  

•  $\left(2.25,\ 4.5\right)$  

•  $\left(-.5,\ -7.5\right)$  

•  $\left(5,6\right)$  

Absolute vs Relative

If multiple Relative Maximums exist on a curve, the one with the largest y value is the Absolute Maximum. The opposite occurs when looking for the Absolute Minimum.

Relative Max not Absolute @ y=-5; (0,-5)

Other y values are larger

Has an Absolute Mim. @ y =-10; (-1,-10)

No other y value is lower than -10

Fill in the Blanks

Multiple Choice

What is the absolute minimum?

• $Does\ not\ exist$

• $\left(-3,\ -2\right)$

• $\left(2,\ 0\right)$

• $\left(-\infty,-\infty\right)$