Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

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Presentation transcript:

Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH From left to right

1 2 Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH f ’(x) > 0 for all x in I 2 f(x) increasing Increasing\Decreasing f ’ (x) < 0 for all x in I f(x) decreasing

Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH How to find local max and local min

_ _ + + 1 2 1 2 Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH First Derivative Test: 1 _ + 2 First Derivative Test: 1 _ + 2

Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH _ + + + + + + + _ _ + + _ + + +

Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

_ _ + + 1 2 1 2 Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH First Derivative Test: 1 _ + 2 First Derivative Test: 1 _ + 2

Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH _ + + + + + + + _ _ + + _ + + +

Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH Example: Find all local max and local min

Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH Example: Find all local max and local min