Concavity and Points of Inflection

Concavity

'The curvature of a graph'

Concave Up

• f looks 'U' shaped

• f ' is increasing

• f " > 0

Multiple Choice

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

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

• $$\left(1,\infty\right)$$

• $$\left(-1,\infty\right)$$

• $$\left(-1,\infty\right)$$

Concave Down

• f looks 'n' shaped

• f ' is decreasing

• f " < 0

Multiple Choice

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

• $$\left(-\infty,-1\right)$$
  

• $$\left(-\infty,1\right)$$

• $$\left(1,\infty\right)$$

• $$\left(-1,1\right)$$

Poll

Where the graph changes concavity is called the...

• Point of Interest

• Point of Inflection

• Point of Concavity

Multiple Choice

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

• True

• False

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