Marking Period 1 Test 2

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

• 6 -x
• 3x² +3y² 
• −x²/y²
• 0

Find dy/dx
xy+y²=2

• -y/(x+2y)
• y/(x+2y)
• -3y/x
• -3x/y

Find dy/dx at a given point.

• 5/4
• 4/5
• 1
• -5

Air is being pumped into a spherical balloon at a rate of 5 cm³/min. Determine the rate at which the radius of the balloon is increasing when the diameter of the balloon is 20 cm.

If a function's FIRST derivative is negative at a certain point, what does that tell you?

• The function is increasing at that point
• The function is decreasing at that point
• The concavity of the function is up at that point
• The concavity of the function is down at that point

Over what intervals is f(x) decreasing?

• (-∞, -1) ∪ (1, ∞)
• (-∞, -√3) ∪ (0, √3)
• (-1, 1)
• (-√3, 0) ∪ (√3, ∞)

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

Identify the critical points of the following function:
g(x)=2x³-3x²

• x=-1,1
• x=0,0
• x=0,-1
• x=0,1

• A relative maximum at x=a

• A relative minimum at x=a

• No relative extrema at x=a

• A vertical tangent line at x=a