3.1 to 3.8 Calculus Exam

Find dy/dx by Implicit Differentiation 
x³ +y³  = 36

• 6 -x
• 3x² +3y² 
• −x²/y²
• 0

A spherical snowball is rolled in fresh snow, causing it to grow so that its radius increases at a rate of 2 in/sec. How fast is the volume of the snowball increasing when the radius is 2 in?

Tags

CCSS.HSG.GMD.A.3

The position of an object is given as a function of time by x = 3t² + 5t³ - 2t
What is the acceleration of the object at time t = 2 s?

• 64 m/s/s
• 60 m/s/s
• 66 m/s/s
• 70 m/s/s

Find the intervals of concavity for

f(x) = x² + 2x + 1.

• concave up: (-∞,∞)

• concave down: (-∞,∞)

• concave up: (2, ∞)

  concave down: (-∞,2)

• concave up: (-∞,2)

  concave down: (2, ∞)

Given the function f(x)=3x⁴-2x³-9x², find the relative minimum values. Check all that apply.

• -1

• 0

• 1.5

• -1.5

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSA.APR.B.3

Given the position function s(t) = - t³ + 26t² - 169t, determine if the particle is speeding up or slowing down when t = 2.

• Speeding up

• Slowing down

A certain medical procedure requires that a balloon be inserted into the stomach and then inflated. Model the shape of the balloon by a sphere of radius r. If r is increasing at the rate of 0.3 cm/min, how fast is the volume changing when the radius is 4 cm?

• 15.08 cm³/min
• 268.08 cm³/min
• 60.32 cm³/min
• 6.03 cm³/min

What are the extrema of the graph?

• Max = (2, -3), (1, 2)

  Min = (-3, -1), (-1, 4)

• Max = (-3, -1), (-1, 4)

  Min = (2, -3), (1, 2)

• Max = (-1, -3), (4, -1)

  Min = (-3, 2), (2, 1)

• Max = (-3, 2), (2, 1)

  Min = (-1, -3), (4, -1)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSA.REI.D.10

What are the decreasing intervals on the graph?

• (-∞, 0) & (-4, ∞)

• (-∞, -1) & (1, ∞)

• (-∞, -2) & (2, ∞)

• (-∞, 0) & (4, ∞)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSA.REI.D.10

Find where absolute maximum of f(x) on the interval [-1, 2]. 

• -1
• 0
• 1
• 2