Derivatives - Properties of Curves

When you are finding the instantaneous rate of change at a single point, you are finding the slope of the (a)   line at that point.

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CCSS.HSF-LE.A.1B

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CCSS.HSF.IF.B.4

Given the following graph with tangent lines, at which

x-value is the derivative equal to zero?

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CCSS.HSF.TF.A.4

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6

• undefined

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CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSG.GPE.B.5

If a function has a derivative that is negative, what does that tell you?

• The function is increasing
• The function is decreasing
• The concavity of the function is up
• The concavity of the function is down

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CCSS.HSF.IF.B.4

The image displays the ______

• Limit definition of the first derivative

• The bane of my existance

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CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

If f'(x) = 0 what does that imply about the x value?

• It is a critical point, it is a possible max, min, or point of inflection.

• That the limit does not exist.