Derivatives Review Game

Find the derivative of
 $f\left(x\right)=-\frac{2}{3}x^3-\frac{1}{2}x^2+9x$  

•  $-2x^2-x+9$  
  

•  $-2x^3-x^2+9x$  
  

•  $-\frac{2}{12}x^4-\frac{1}{6}x^3+\frac{9}{\ 2}x^2$  
  

•  $-2x^4-x^3+9x^2$  
  

Which of the following is the derivative of  $y=\left(3x^4-7\right)\left(5x^2+1\right)$  

•  $\left(12x^3\right)\left(10x\right)$  
  

•  $\left(3x^4-7\right)\left(10x\right)+\left(12x^3\right)\left(5x^2+1\right)$  
  

•  $\left(3x^4-7\right)\left(10x\right)-\left(12x^3\right)\left(5x^2+1\right)$  
  

•  $\frac{3x^4-7}{10x}+\frac{12x^3}{5x^2+1}$  
  

Tags

CCSS.HSA.APR.A.1

Find the derivative of 
 $f\left(x\right)=xe^x$  

•  $f'\left(x\right)=e^x$  

•  $f'\left(x\right)=2xe^x$  

•  $f'\left(x\right)=e^x-xe^x$  
  

•  $f'\left(x\right)=e^x+xe^x$  
  

Check off all of the words that also mean derivative.

• instantaneous rate of change

• average rate of change

• slope at a point

• slope of a secant line

• slope of a tangent line

Finding the derivative of 
 $f\left(x\right)=xe^x$  requires the...

• power rule

• product rule

• quotient rule

• chain rule

Given the table of R(t), estimate R'(10).

• 33

• 42

• 9

• 9/4

• 9/10

Water flows into a tank for 24 hours. R(t) represents the gallons of water in the tank at t hours. What does R'(t) represent? Check all that apply.

• the amount of water in the tank in gallons

• the rate of change of the water at t hours

• the speed of the water flow at t hours

• gallons per hour

Describe how to estimate f'(1) given the table of values for f(x) = 0.5x^3 - 2.

Is the above function differentiable for all values of x? Why?

• Yes, the slope of the tangent line can be calculated for all values of x.

• Yes, the function is continuous for all values of x so the function is differentiable.

• No, the function has a sharp turn in the first quadrant so if is not differentiable.

• No, the function is discontinuous so it is not differentiable.

Tags

CCSS.HSA.REI.D.10

In which quadrant of the graph above will there be a value of x that is non-differentiable?

• 1

• 2

• 3

• 4

Tags

CCSS.8.F.A.3