Sec 4 3 HOW DERIVATIVES AFFECT THE SHAPE

Sec 4. 3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH From left to right

Sec 4. 3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH IncreasingDecreasing 1 f ’(x) > 0 for all x in I f(x) increasing 2 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

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

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