First Derivative Test
Second Derivative Test
Absolute Max and Min
Limits
Applications
100

What does f'(x)>0 tell us about the original function?

The function is increasing.

100

What does  f''(x)<0 tell us about the original funtion?

The function is concave down.

100

Identify the absolute maximum

16

100

lim_(x->9) (x-9)/(x^2-81)


1/18

100

What is the domain of the price-demand function?

p=350-x/40

0<=x<=14,000

200

Identify the local extrema of the function.

local max: 16

local min: 0

200

Sketch a graph that meets the following conditions.

 f'(x)<0 

f''(x)>0

200
On a closed interval [a,b], what values do you need to test to locate the absolute extrema?

the endpoints and critical numbers

200

lim_(x->4) (x^2+x-20)/(x-4)

9

200

A car rental agency rents 200 cars per day at a rate of $20 per day. For each $1 increase in rate, 5 fewer cars are rented.

Write the revenue function for the number of cars rented.

R(x)=(200-5x)(20+x)

R(x)=-5x^2+100x+4000

300

Find the intervals of increase and decrease.

f(x)=4+8x-x^2

increasing 

(-oo,4)

decreasing 

(4, oo)

300

Identify the intervals on which the function

f(x)=x^3-21x^2+17x+7

 is concave up and concave down.

Concave down

(-oo, 7)

Concave up 

(7, oo)

300

Find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x-values at which they occur.

 g(x)=x^2+4    [1,5]

absolute max of 29 at x=5

absolute min of 5 at x=1

300

lim_(x->oo) (x^11)/(lnx)

oo

300

A company manufactures and sells x cellphones per week. The weekly price-demand and cost equations are given below.

  p=600-0.5x     C(x)=20,000+140x 

Write the profit function for the number of cell phones produced and sold.

P(x)=-0.5x^2+460x-20,000

400

Find the local extrema of 

g(x)=x^3-75x-3

Local max of 247 at x=-5

Local min of -253 at x=5

400

Identify the intervals on which the function

f(x)=x^4-2x^3

 is concave up and concave down.

Concave down

(0,1)

Concave up 

(-oo,0), (1,oo)

400

Find the absolute minimum of 

 f(x)=9x^3-4 

no absolute minimum

400

lim_(x->0) (e^(5x)-1)/(x^2+x)

5

400

A deli sells 960 sandwiches per day at a price of $8 each.

A market survey shows that for every $ 0.10 reduction in the price, 20 more sandwiches will be sold. How much should the deli charge in order to maximize revenue?


$6.40

500

Find the intervals of increase and decrease.

f(x)=5/(x^3+8)

decreasing 

(-oo,oo)

500

Determine the point(s) of inflection.  Write as ordered pairs.  No rounding ;)

f(x)=-x^6+42x^5-42x+13

(0, 13)

(28, 240943989)

500

Find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x-values at which they occur.

 f(x)=x^4-8x^2+16   [-1,3]

absolute max of 25 at x=3

absolute min of 0 at x=2

500

lim_(x->4) (sqrt(x)-2)/(x^2-16)

1/32

500

A company manufactures and sells x cellphones per week. The weekly price-demand and cost equations are given below.

 p=600-0.5x   C(x)=20,000+140x

What price should the company charge for the phones maximize the weekly revenue? 

$300