Concavity - AP Calculus - Lecture Notes, Study notes of Calculus

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Calculus Section 3.4A Notes Learning Targets... 1. Use ist Derivative Test to determine concavity 2. Use 2nd Derivative Test to determine concavity 3. Use 2nd Derivative Test to determine extrema LT: Use 1* Derivative Test to determine * lf FGWiS increasing, the graph of o What does it mean that f’(x) is increasing? + if PGS decreasing the graph of fix)is Concave down Is the function f(x) = x* concave up or concave down? ) £Cx) =2x Vee me? “NERS My ertenhela AOR) cone. * aemwhere LT: Use 2™ Derivative Test to determine concavity Graph the function and its derivative on the calculator. 2) f(x) =x? cx) = 3x” £" Cx) i ea e Where is the graph of f concave up/down? e Graph the 2™ derivative. How does this relate to the other 2 graphs? e if , the graph of f(x) is e If , the graph of f(x) is . e If or undefined, thereisa point of inflection (where the concavity changes from up to down or vice versa). o Nocool name for zeros a Inflection change isn’t necessarily a point v 1/2