Calculus: Chapter 3 Jeopardy

Derivatives

100

y = 3x⁴-5x²+x-4

y' = 12x³-10x+1

200

y=x³/4+6x^2.5+8 ⁴√x

y' = 3/4x²+15x^1.5+2x^-3/4

300

y=x/6 +6/x

y' = 1/6 - 6x^-2

400

y=(x+6)(3x-1)

y' = 6x+17

Antiderivatives

100

y' = 2x³-4x+7

y = .5x⁴-2x²+7x+C

200

y' = 0.9x²+6x-1

y = 0.3x³+3x²-x+C

300

y' = 0.5 sin(x/2)

y = - cos(x/2) + C

400

y' = √6x+5

y=(1/9)(6x+5)^3/2+C

Disp, Vel, Acc

100

d(t) = 5 sin (2 π t)+6
Find v(t).

v(t) = 10 π cos(2 π t)

200

d(t) = 5t1/3+10t
Find a(t).

a(t) = -10/9t^-5/3

300

d2y/dt2= 12t2
Find y when t = 2, dy/dt =42, and y = 34.

y = t⁴+10t-2

400

d(t) = t3-8t2+3t-5

At t = 2, is the particle speeding up or slowing down. Justify.

Speeding up, because v(2) is negative and a(2) is negative.

Chain Rule

100

y=-3sin(x⁴)

y' = -12x³cos(x⁴)

200

y=10cos(4(t-25))+8

y' =-40sin(4(t-25))

300

y=sin⁵(x²)

y' = 10xsin⁴(x²)cos(x²)

400

y=8/√(9-x²)

y' = 8x(9-x²)^-3/2

Etc.

100

Give the definition of f '(x).

lim_h→0(f(x+h)-f(x))/h

200

Give the equation of the tangent to y = √(3x-2)
at x = 6.

y - 4 = 3/8 (x-6)

300

Name two instances in which the derivative 
is not defined.

 a cusp,
function has a vertical tangent,
or function is not defined

400

Find
limh→0(cos(3(x+h))-cos(3x))/h

-3 sin (3x)