1 2 Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH Concavity Test

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Presentation transcript:

1 2 Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH Concavity Test f’’(x) > 0 for all x in I 2 f(x) concave Up Concavity Test f’’(x) < 0 for all x in I f(x) concave Down

1 2 Example: Discuss the curve with respect to concavity, Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH 1 f’’(x) > 0 for all x in I 2 f(x) concave Up Concavity Test f’’(x) < 0 for all x in I f(x) concave Down Example: Discuss the curve with respect to concavity,

Concavity Test 1 f’’(x) > 0 for all x in I f(x) concave Up

Concavity Test 1 f’’(x) < 0 for all x in I f(x) concave Down

Find all inflection points of Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH Example: Find all inflection points of

Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

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Example: x^(2n) true or false

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