critical numbers: 2nd derivative · the second derivative test the point where a function changes...

CRITICAL NUMBERS: 2nd Derivative tangents lines above the curve CONCAVE DOWN tangents lines below the curve CONCAVE UP CRITICAL NUMBERS

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CRITICAL NUMBERS: 2nd Derivative

tangents lines above the curve

CONCAVE DOWN

tangents lines below the curve

CONCAVE UP

CRITICAL NUMBERS

concave up

concave down

critical number f''

zero slopes

concave down

concave up

ZERO SLO

ZEROSLOPE

Page 5: CRITICAL NUMBERS: 2nd Derivative · The Second Derivative Test The point where a function changes from: Concave Up to Concave Down OR Concave Down to Concave Up is called a Point

Page 6: CRITICAL NUMBERS: 2nd Derivative · The Second Derivative Test The point where a function changes from: Concave Up to Concave Down OR Concave Down to Concave Up is called a Point

Page 7: CRITICAL NUMBERS: 2nd Derivative · The Second Derivative Test The point where a function changes from: Concave Up to Concave Down OR Concave Down to Concave Up is called a Point

Page 8: CRITICAL NUMBERS: 2nd Derivative · The Second Derivative Test The point where a function changes from: Concave Up to Concave Down OR Concave Down to Concave Up is called a Point

f"(x)=6x0=6xx=0

Page 9: CRITICAL NUMBERS: 2nd Derivative · The Second Derivative Test The point where a function changes from: Concave Up to Concave Down OR Concave Down to Concave Up is called a Point

Page 10: CRITICAL NUMBERS: 2nd Derivative · The Second Derivative Test The point where a function changes from: Concave Up to Concave Down OR Concave Down to Concave Up is called a Point

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