1. SECT 3-8B RELATING GRAPHS Handout: Relating Graphs

2. Relating Graphs If the function is increasing, then the graph of the derivative is above the x-axis If the function is decreasing, then the graph of the derivative is below the x-axis If the function has extrema, then the graph of the derivative is crossing the x-axis If the function changes concavity, then the graph of the derivative has an extrema

3. Relating Graphs If the graph of the derivative is above the x-axis (positive) then the function is increasing If the graph of the derivative is below the x-axis (negative) then the function is decreasing If the graph of the derivative has an zero then the function has a possible max or min

4. Relating Graphs If the graph of the derivative is decreasing (negative slope) then the function is concave down If the graph of the derivative is increasing (positive slope) then the function is concave up If the graph of the derivative has an extrema then the function has a possible point of inflection

5. Using Number lines Antiderivatives:f ′ graph → f graph 1. Make an f ′ number line by using the location or position of the points on the f ′ graph. This does not involve the slopes of f ′. 2. Make an f ′′ number line by using the slopes of the f ′ graph. 3. Combine information from both number lines to graph f. If no starting point is given, you are free to shift the graph vertically.

6. 7) The graph of is given above. The domain of f is a) For what value(s) of x, is the graph of f increasing? Justify your answer. b) For what value(s) of x, does the graph of f have a relative maximum? Justify your answer

7. 7) The graph of is given above. The domain of f is c) For what value(s) of x, is the graph of f concave up and concave down? Justify your answer. d) For what value(s) of x, does the graph of f have inflection points? Justify your answer.

8. 7) Sketch a possible graph of

9. 8) The graph of f ′ is shown, sketch a possible graph of f with a starting point of (0,1)

10. 9) Use the graph of f ′ shown to sketch a graph of f ′′ and a possible graph of f. f ′′ f ′f

11. Homework Worksheet 3-8B