Applications of Derivatives Review

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

• 6 -x
• 3x² +3y² 
• −x²/y²
• 0

Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The radius of the spill increases at a rate of 5 m/min. How fast is the area of the spill increasing when the radius is 5 m?

• 50π m²/min

• 47π m²/min

• 52π m²/min

• 40π m²/min

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

If the position of a particle is represented by s(t) = -t² + 1, what is its position at t = 1? 

• Position = 0
• Position = 1
• Position = 2
• Position = -1 

If the position function for a particle is s(t) = -t² - t, what is the instantaneous velocity function for the particle? 

• v(t) = -2
• v(t) -2t - 1 
• v(t) = t³
• v(t) = -t

If the position of a particle is represented by s(t) = -t² + 1, what is its instantaneous velocity at t = 1?  

• Velocity = 0
• Velocity = 1
• Velocity = -1
• Velocity = -2

To find the velocity function, you need the

• first derivative

• second derivative

• third derivative

• original function

Given x(t)=t³-4t²+7, what is the initial position?

• 11
• -10
• 7
• 0

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