AP Calc AB Unit 5

Increasing

when f'(x) > 0

Decreasing

when f'(x) < 0

Critical Point

x value where f'(x) = 0

Local Maximum

point where the function changes from increasing to decreasing

Local Minimum

point where the function changes from decreasing to increasing

Absolute Maximum

highest value of a function on a given interval

Absolute Minimum

lowest value of a function on a given interval

Closed Interval Method

find absolute extrema by checking critical points and endpoints

First Derivative Test

use sign changes of f'(x) to identify local max and min

Second Derivative Test

if f'(c) = 0 and f''(c) > 0 then local min if f''(c) < 0 then local max

Concave Up

when f''(x) > 0 the graph curves upward

Concave Down

when f''(x) < 0 the graph curves downward

Point of Inflection

point where concavity changes and f'' changes sign

Second Derivative

derivative of f'(x) used to determine concavity

Relative Extrema

local maximums and minimums

Graph Behavior from f'

f'(x) > 0 increasing f'(x) < 0 decreasing

Graph Behavior from f''

f''(x) > 0 concave up f''(x) < 0 concave down