Level 570
Level 572

#### 22 words 0 ignored

Ready to learn
Ready to review

## Ignore words

Check the boxes below to ignore/unignore words, then click save at the bottom. Ignored words will never appear in any learning session.

**Ignore?**

First Derivative test

If the first derivative changes from negative to positive at c then f has a relative minimum at the point (c,f(c)) If it goes from positive to negative it is a relative maximum

concavity

a graph is concave up is the tangent lines are below the graph; a graph is concave down if the tangent lines are above the graph

Limits at infinity

The dependent variable approaches a finite number as the independent variable becomes arbitrarily large

Second derivative test

If the second derivative is greater than zero then the function has a relative minimum

Asymptotes

y=±b/a(x-h)+k

Non differentiable points

Result of change in concavity and Increasing or decreasing. Example: Increasing Concave down- Decreasing Concave Up

Decreasing-Increasing

Relative Minimum

Increasing-Decreasing

Relative Maximum

point of inflection

When f '(x) changes from increasing to decreasing or decreasing to increasing, f(x) has a

Process for sketching

1.Solve for intercepts

Rolle's Theorem

If f(x) is continuous on [a,b], differentiable on (a,b), and f(a) = f(b), then there exists a point c∈(a,b), where f '(c) = 0.

Y'=0 or is undefined

Y has a critical point

Y is increasing

Y' > 0

Y is decreasing

Y' < 0

Y has a local minimum

Y' changes from - to +

Y has a local maximum

Y' changes from + to -

Y is concave up

Y' is increasing or Y'' > 0

Y is concave down

Y' is decreasing or Y'' < 0

Y has a point of inflection

Y' switches from increasing to decreasing or decreasing to increasing. Y''switches from + to - or - to +

Y has absolute max or min

Check all critical points and endpoints

Asymptote

An imaginary line on a graph that acts as a boundary line.

Holes

when same factor occurs in numerator and denominator