Ap Calculus Ab.db

Front 1

definition of a critical value

Back 1

f'(c)=0 or if f'(c) does not exist than c is called a critical value of f

Front 2

Test for increasing and Decreasing Functions

Back 2

1. a function f is increasing on an interval if f'(x) > 0 on that interval
2. A function f is decreasing on an interval if f'(x)<0 on that interval

Front 3

First Derivative Test= relative minimum

Back 3

C=critical value of a function f

1.If f'(x) changes from negative to positive at c, then f(c) is a relative minimum of f

Front 4

First Derivative test= relative maximum

Back 4

C= critical value of a function f

if f'(c) changes from positive to negative at c, then f (c) is a relative maximum of f

Front 5

First derivative test= no relative max or min

Back 5

f'(x) does not change signs at c

Front 6

relative extrema

Back 6

relative extrema only occur at critical values but all critical values are not necessarily relative extrema

Front 7

Extreme Value Theorum

Back 7

If f is continuous on the closed interval [a,b], then f has botha minimum and a maximum on the interval

Front 8

Finding extrema on a closed interval

Back 8

1. find values of f at the critical numbers of f in (a,b)
2. Find the values of f at the ENDPOINTS of the interval
3. the least of these values is the minimum, the greatst is the maximum

Front 9

Test for concavity=concave up

Back 9

if f''(x)>0 for all x in an open interval I, then the graph of f is concave upward on I

Front 10

Test for concavity= concave down

Back 10

if f''(x)<0 for all x in an open interval I, then the graph of f is concave downward on I

Front 11

definition of points of inflection

Back 11

a point P on a curve y=f(x) is called a point of inflection if f is continues on P and the curve changes from concave upward to concave downward or vice versa

If (c, f(c)_ is a point of inflection of the graph of f, then either f''(x)=0 or f is not differentiable at x=c

Front 12

Second Derivative test= relative minimum

Back 12

f'(c)=0 and f''(x) exists on an open interval containing c
1. if f''(c)>0, the f(c) is a relative minimum

Front 13

Second derivative test= relative maximum

Back 13

f'(c)=0 and f''(x) exists on an open interval containing c
if f''(c) <0, then f(c) is a relative maximum

Front 14

Second Derivative test=failed

Back 14

f'(c)=0 and f''(x) exists on an open interval containing c
if f''(c)=0 the test fails use the first derivative test

Front 15

sketching a curve

Back 15

1. domain
2. intercepts
3. symmetry
4. asymptote
5. intervals of increasing or decreasing
6. relative maximum and relative minimum
7. points of inflection and concavity

Front 16

domain

Back 16

what are the values of x for which f(x) is defined

Front 17

intercepts

Back 17

x intercept= let y=0 and solve for x
y intercept= let x=0 and solve for y

Front 18

symmetry on the y axis

Back 18

if f(-x)=f(x) then f is an even function and the curve is symmetric about the Y AXIS