Calculus

# Applying derivatives to analyze functions

- Using the mean value theorem
- Extreme value theorem, global versus local extrema, and critical points
- Determining intervals on which a function is increasing or decreasing
- Using the first derivative test to find relative (local) extrema
- Using the candidates test to find absolute (global) extrema
- Determining concavity of intervals and finding points of inflection: graphical
- Determining concavity of intervals and finding points of inflection: algebraic
- Using the second derivative test to find extrema
- Sketching curves of functions and their derivatives
- Connecting a function, its first derivative, and its second derivative
- Solving optimization problems
- Exploring behaviors of implicit relations
- Calculator-active practice

## Explore other Calculus Topics

GQ

Calculus

## General Calculus Q&A

0 Sessions

Lc

Calculus

## Limits and continuity

52 Sessions

Dr

Calculus

## Differentiation: definition and basic derivative rules

15 Sessions

Df

Calculus

## Differentiation: composite, implicit, and inverse functions

9 Sessions

Cd

Calculus

## Contextual applications of differentiation

10 Sessions

Af

Calculus

## Applying derivatives to analyze functions

7 Sessions

Ic

Calculus

## Integration and accumulation of change

10 Sessions

De

Calculus

## Differential equations

5 Sessions

Ai

Calculus

## Applications of integration

7 Sessions

Pf

Calculus

## Parametric equations, polar coordinates, and vector-valued functions

2 Sessions

Is

Calculus

## Infinite sequences and series

2 Sessions

AC

Calculus

## AP Calculus

82 Sessions