1. W-UP COPY statements then state true for false, if false, sketch a graph or state why. 1) If a function is continuous then it is differentiable. 2) If a function is differentiable then it is continuous.

2. SWBAT DETERMINE CONCAVITY, FIND INFLECTION POINTS, GRAPH FUNCTIONS, AND USE THE SECOND DERIVATIVE TEST. 14.3: CONCAVITY; THE SECOND DERIVATIVE TEST

3. CONCAVITY: Concave Up: Throughout (a,b), the tangent lines to the graph lie below f. Concave Down : Throughout (a,b), the tangent lines to the graph lie above f. Let f denote a function that is differentiable on the interval (a, b).

4. TEST FOR CONCAVITY: LET Y = F(X) BE A FUNCTION AND LET F’’(X) BE ITS SECOND DERIVATIVE. If f’’(x) > 0 for all x in the interval (a,b), then the graph of “f” is concave up on (a,b). If f’’(x) < 0 for all x in the interval (a,b), then the graph of “f” is concave down on (a,b).

5. -∞<x<00<x<66<x<∞ (-1)(3)(7) F’(-1) is PosF’(3) is NegF’(7) is Pos IncreasingDecreasingIncreasing

6. PERFORM THE SECOND DERIVATIVE TEST TO FIND THE POINTS OF INFLECTION AND TEST FOR CONCAVITY: (*POI IS WHERE THE GRAPH CHANGES CONCAVITY) (-∞,3)(3,∞) F’’(2) is negF’’(4) is Pos Concave DownConcave Up

7. WHEN G(X) IS F’(X) AND H(X) IS F’’(X)

8. (-∞,-1)(-1,0)(0,∞) F’’(-2) is posF’’(-.5) is NegF’’(1) is Pos Concave UpConcave DownConcave Up

9. HW: WS 14.3 1-12 All 13-27 Odd