How much do you remember about curve sketching?

To find the concavity of a function you use the ____

• first derivative test

• slope-intercept form

• second derivative test

• third derivative test

The first derivative test helps us figure out if ____

• the graph is even or odd

• none

• it is concave up or concave down

• the slope is positive or negative

What is the point of inflection?

• A point where the curve intersects the x-axis

• A point where the curve changes color

• A point where the curve intersects the y-axis

• A point on a curve where the curvature changes direction

For a function g(x), g''(3)=-8 indicates that g(x) is ____________ at x=3.

• decreasing

• increasing

• concave up

• concave down

For a function f(x), f'(-3) = 5 indicates f(x) is ___________ at x=-3.

• decreasing

• concave up

• increasing

• concave down

Find the point of inflection for y=x³+6x²+9x

• -3

• -2

• -1

• 0

When f'(x) changes from a negative to a positive there is a ____

• Maximum

• Minimum

Identify the concavity

• concave up only

  
  

• concave down only

  
  

• both concave up and down

  
  

• none

Find the second derivative of
f(x) = x² + e^x - cosx

• f"(x) = 2 + e^x + cosx

• f"(x) = 2x + e^x + cosx

• f"(x) = 2x + xe^x - cosx

• f"(x) = 2 + e^x + sinx

Which of the following could be the graph of f ' , the derivative of f ?

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