Extrema and Function Analysis (3.2 CA)

The highest/lowest point for the entire function/graph.

Any peak in the function

The part that tends to infinity or negative infinity of the graph

A point higher/lower than its surrounding values. (a peak)

The second highest/lowest point in the graph

$\left[\infty,-1\right]\cup\left(2,\infty\right)$

$\left(-\infty,\infty\right)$

$\left(-4,-1\right]\cup\left(2,\infty\right)$

N/A

(2, -4) is an Absolute Min

(-1,1) is an Absolute Max

$\infty$

N/A

(2, -4) is a Local Min

(-1,1) is an Local Max

(-2,-1) is a Local Min

Increasing:  $\left(-2,\ 1\right)\cup\left(2,\ \infty\right)$  

Decreasing:  $\left(-\infty,\ -2\right)$  

It's a constant function

Increasing:  $\left(-2,\ \infty\right)$  

Decreasing:  $\left(-\infty,\ 2\right)$  

$x+5\ge0$

$x+5>0$

$x^2+2\le0$

All real numbers

Absolute Min at

(0.098, -2.247)

N/A

Absolute Max at

(-4.098, 7.025)

Absolute Min at

(-5,0)

Local Min at

(0.098, -2.247)

N/A

Local Max at

(-4.098, 7.025)

Local Min at

(-5,0)

Increasing:
$\left(-5,\ -4.098\right)\cup\left(0.098,\ \infty\right)$

Decreasing:
$\left(-4.098,\ 0.098\right)$

Increasing: $\left(-5,\ \infty\right)$

the function is constant