Assessment

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

• 6 -x
• 3x² +3y² 
• −x²/y²
• 0

Find dy/dx by Implicit Differentiation 
x + 4y = 1

• -1/4
• -1 
• 4
• 1 

Find dy/dx by Implicit Differentiation
2xy³ - x²y = 2

• 2xy - 2y³
• 2y(x-y²)/x(6y²-x)
• -2y/x
• 2

A rectangular  page is to contain 144 sq. inches of print. the margins on each side are 1 inch. Find the dimensions of the page that would use the least paper

• 16, 16
• 15,15
• 14,14
• 13,13

Colette is starting to clean up after a birthday party. She begins deflating each spherical balloon by puncturing a hole in each. The air leaves the balloon at a constant rate of 2 cm³/sec. How fast is the diameter changing when the diameter is 8 cm?

• -1/(16pi) cm/sec

• -1/16 cm/sec

• -1/(4pi) cm/sec

• 1/(4pi) cm/sec

We need to enclose a field with a fence. We have 500 feet of fencing material and a building is on one side of the field so we won't need any fencing on that side. Determine the dimensions of the field that will enclose the largest area.

• x=250 ft, y=125 ft
• x=150 ft, y=200 ft
• x=125 ft, y=100 ft
• x=200 ft, y=150 ft

FInd the derivative:
f(x) = (-2/3)x³ - (1/2)x² + 9x

• -2x² - x + 9
• -2x² + x + 9
• 2x² - x + 9
• 2x² - x - 9

Find the second derivative of the function:
f (x) =  2x - 5x⁶

• f ''(x)= 2 - 30x
• f ''(x) =  2-30x⁵
• f ''(x) = -30x⁵
• f ''(x) = -150x⁴

An absolute maximum must occur at a critical point or at an endpoint.

• True
• False

A critical number, c, or a function f is a number in the domain of f such that:

• f'(c) = 0
• f'(c) is undefined
• f'(c) = o or f'(c) is undefined
• None of the above