Points of Inflection Lesson

3 Slides • 5 Questions

1

Concavity

'The curvature of a graph'

2

Concave Up

f looks 'U' shaped
f ' is increasing
f " > 0

3

Multiple Choice

Over what intervals will the second derivative of f(x) be positive?

1

$\left(-\infty,1\right)\ and\ \left(1,\infty\right)$

2

$\left(1,\infty\right)$

3

$\left(-1,\infty\right)$

4

$\left(-1,\infty\right)$

4

Concave Down

f looks 'n' shaped
f ' is decreasing
f " < 0

5

Multiple Choice

Over what intervals will the second derivative of f(x) be negative?

1

$\left(-\infty,-1\right)$

2

$\left(-\infty,1\right)$

3

$\left(1,\infty\right)$

4

$\left(-1,1\right)$

6

Poll

Where the graph changes concavity is called the...

Point of Interest

Point of Inflection

Point of Concavity

7

Multiple Choice

All 'pretty polynomial' graphs have a point of inflection.

1

True

2

False

8

Poll

Check the statements that make the most sense to you...

The graph is always increasing

The graph has no relative extrema

The graph has one point of inflection

The graph has two vertical asymptotes

The graph has one horizontal asymptote

Concavity

'The curvature of a graph'

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