Calculus

Differentation

100

F(x)= 6x^2 + 3x^6 + 9

What is 12x + 18x^5

200

f(x) = √(x^2 + 9) + 9x^2 + 18x + 10

What is x ______ + 18x + 18 √(x^2 + 9)

300

f(x) = 5xsec(x)

What is 5xsec(x)tan(x)+5sec(x)

400

f(x) = 7cot(x^2)

What is −14xcsc^2(x^2)

500

f(x) = (sinx/cosx) + 2xsec(x^2)

What is 4x^2sec(x^2)tan(x^2)+2sec(x^2) + sec^x

Integration

100

∫ 6x^2 + 9x + 7

What is 2x^3 + 9/2x^2 + 7x + C

200

∫ 4/(√2x)^3

What is 6x^2/3

300

∫ sec^2(2x^2+3x+5)+csc^2(2x^2+3x+5)

What is 1/2tan(2x+5)- cot(2x+5) + C

400

What are the trig identities of the following equations sin(x) cos(x) sec^2(x) csc^2(x)

What is -cos(x) + C sin(x) + C tan(x) + C -cot(x) + C

500

∫x√(x^2+1)

What is 1/3(x^2+1)^3/2

Increasing/DecreasingandConcavity

100

Finding the critical point and increasing and decreasing intervals f(x) = 3x^5+6x^3 + 7x + 2

What is Not Applicable

200

Find the inflection points f(x) = 1/2x^4

What is x=0

300

Find the inflection point(s) and concavity of: y = x^3 -3x^2 +4

What is x=1 Concave up: (1, ∞) Concave down: (−∞, 1)

400

Find the critical points and inflection points of: f(x)=x^3 -2x^2 -2

What is Critical Points: x= 0, x=4/3 Inflection Points: x = 2/3

500

Find increasing, decreasing, and concavity. You must also list the critical point and the inflection points. y= x^4 + x^3 -3x^2 +1

What is Critical Points: x = .906,0,-1.6558 Increasing: (-1.6558,0), (.906,∞) Decreasing: (-∞, -1.6558), (0,.906) Inflection Points: x = -1, .5 Concave up: (−∞, −1), (1/2, ∞) Concave down: (−1,1/2)