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When does a derivative not exist?
Differentiability When does a derivative not exist?
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Polynomial: Derivative exists everywhere
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Three reasons a derivative does not exist
Function Not Continuous
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2. Vertical Tangent
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3. Cusp or Corner
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Locate x values for each.
Vertical Tangent Cusp or Corner Discontinuity Which points on the interval (-4,5) are continuous but not differentiable?
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Can you locate any horizontal tangents
Can you locate any horizontal tangents? What does the derivative equal at a horizontal Tangent? Estimate the following: f’(-1)= f’(0)= f’(-2)=
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Find the equation of the line that is tangent to each function
Find the equation of the line that is tangent to each function. (point slope form) 𝑓 5 =3 𝑓 ′ 4 =−2 𝑔(−1)=8 𝑔 ′ −1 =9 ℎ 5 =3 ℎ ′ 4 =−2
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Homework Page 2
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Name as many terms/notation that mean the same as (or are associated with) “derivative” as you can.
Here are a few: Instantaneous Rate of Change Slope Tangent Slope of a tangent line f’(x) dy/dx y’ Velocity or speed Quizlet: cards/
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What is the difference between:
The equation of the line tangent to f(x) and the slope of the tangent line to f(x) The Average Rate of Change and the Instantaneous Rate of Change f(2)=3 and f’(2)=3 The slope of the secant and the slope of the tangent Horizontal tangent and Vertical tangent
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Quiz on Wednesday: Average rate of change/slope of a secant line.
“Find the derivative using the definition of derivative.” Yes, it will be on the quiz. I will choose one very similar to those in the video on my blog. The video shows step by step solutions to each. Find an estimated derivative from a graph. Identify points where function is or is not differentiable. Vocab
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