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Derivatives

100

12x^3

36x^2

200

1+7𝑥−3𝑥^2

-6x+7

300

1/4x^3-3x

3/4x^2-3

400

3x^2/3-2x^2+7

2x^-1/3-2

500

13x^4+29x^3-12x^2+4x-52

52x^3+87x^2-24x+4

Integrals

100

∫7x^6-5x^3+4dx

x^7-5/4x^4+4x+C

200

∫e^x + 6√𝑥dx

e^x+4x^3/2+C

300

∫(3x + 2)^2dx

3x^3+6x^2+4x+C

400

∫7cscxcotxdx

-7cscx+C

500

∫3/5x^2/3-9x+1dx

9/25x^5/3-9/2x^2+x+C

Unit Circle

100

sin π/3

√3/2

200

cos 7π/4

√2/2

300

tan 7π/6

√3/3

400

cot π

undefined

500

sec 5π/3

2

Average Value

100

x^3 [1,3]

10

200

4-3x^2 [-1,1]

3

300

1/x [e,2e]

ln2/e

400

6-x^2 [-2,2]

-2

500

x-2√x [0,4]

-2/3

Economics

100

What does this equation represent

C'(x)=R'(x)

Maximum profit

200

What is the equation for average cost

C(x)/x

total cost/quantity

300

what is the equation for revenue

xp

quantity x price

400

what is the equation for profit

R(x)-C(x)

revenue-cost

500

the revenue function for a product is R(x)=x(4-.0001x). Find the largest revenue.

40,000