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You know that the first derivative, , tells us the slope and the rate of change of .

  1. What does the second derivative, , tell you about ? What does tell you about ?

    tells us the same thing about that tells us about .

  2. Write equations for and if .


  3. Is getting steeper or less steep at ? At ? Use your derivatives from part (b) to explain your reasoning.

    Consider this: Even though a slope of is steeper than a slope of , if the slope changes from to , then the slope is decreasing.

  4. The values of and can be used to determine concavity at and . Where is concave up? Where is concave down?

    Positive values of the 2nd-derivative indicate that the function is concave up while negative values indicate that the function is concave down.