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

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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Page 1: 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

CRITICAL NUMBERS: 2nd Derivative

tangents lines above the curve

    CONCAVE DOWN

tangents lines below the curve

     CONCAVE UP

CRITICAL NUMBERS

Page 2: 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

concave up

concave down

Page 3: 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

critical number f''

zero slopes

zero slopes

Page 4: 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

concave down

concave up

concave up

ZERO SLO

PE

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