Average vs Instantaneous Rate of Change

• sinx
• -sinx
• -cscx cotx
• sec²x

An objects distance from its starting point at time t is given by the equation
s(t) = t³ - 6t²  - 4. 
What is the speed of the object when its acceleration is 0? 

• 2

• -24

• 22

• 44

If Distance is a function of Time, what is the average rate of change from 6 to 9 seconds?

• 3.3 feet per second

• -10 feet per second

• -3.3 feet per second

• 10 feet per second

A bug begins to crawl up a vertical wire at time t = 0.  The velocity v of the bug at time t, 0 < t < 8, is given by the function whose graph is shown behind this text. At what value of t does the bug change direction? 

• 2

• 4

• 6.5

• 7

The position function x(t)=7t²-18t-7 is given. What is the velocity function?

• v(t)=14t-18

• v(t)=14t+18

• v(t)=18t-14

• v(t)=18t+14
  

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

• m = 0

• f'(x) = -6x - 6

• f'(x) = 6x

• m = -12

Derivative means the same thing as

• slope of the tangent line

• slope of the normal line

• exponent

• slope of the secant line

Find the derivative.

• x⁴ cosx - 4x³sinx

• x⁴ cosx + 4x³sinx

• 4x³cosx

• -4x³cosx

• A
• B
• C
• D

Hint: Split the fraction (Easier than quotient rule)

• A

• B

• C

• D