Derivatives as Rate of Change

Derivatives as Rate of Change

Multiple Choice

Which of the following are ways to find the rate of change?

• change in y over change in x
• rise over run
• subtract y coordinates over subtract x coordinates
• all of the above

Multiple Choice

A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet. What is the average rate of change? 

• 200
• 150
• 300
• 75

Multiple Choice

At what rate did the rain fall?

• 2 cm per hour
• ¹/₄ cm per hour
• ¹/₂ cm per hour
• 4 cm per hour

Multiple Choice

Find the derivative of the given equation
f(x) = x³ + x² + 3

• 3x² + 2x
• 3x + 2x 
• 3x + 2x + 3
• x³ + x² 

Multiple Choice

Find the slope of f(x) = -3x²-6x at x = 1.

• m = 0
• f'(x) = -6x - 6
• f'(x) = 6x
• m = -12

Multiple Choice

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

• v = 0
• v = 1
• v = -1
• v = -2