Related Rates + Other Review

Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the ladder sliding down the wall when the tip of the ladder is 5 ft high?

• 3 ft/sec

• -7.2 ft/sec

• 7.2 ft/sec

• 12

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. If the radius of the outer ripple is increasing at a rate of 2 cm per second, how fast is the area of the ripple increasing when the radius is 5 cm?

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

• 6 -x
• 3x² +3y² 
• −x²/y²
• 0

A spherical snowball melts so that its radius decreases at a rate of 4 in/sec. At what rate is the volume of the snowball changing when the radius is 4 in?

• -262π in³/sec

• -247π in³/sec

• -256π in³/sec

• -263π in³/sec

Brandon is starting to clean up after a birthday party. He 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

Find dy/dx at a given point.

• 5/4
• 4/5
• 1
• -5

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

• 64 m/s/s
• 66 m/s

• 66 m/s/s
• 64 m/s

Where is the graph not differentiable?

• x = -2, -1, 0, 1
• x = -2, -1, 1
• x = -2, -1
• x = -1, 

Tags

CCSS.HSA.REI.D.10

If f '(x) changes from negative to positive, then f(x) has __________ at x.

• a maximum

• a minimum

• no extrema

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

• x = 0 only

• x = 0 and x = - 4

• x = - 4 only

• x = - 4, x = 0, and x = 4