AP Calc Unit 2 & 3: Differentiation

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7 Terms

1
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What is the definition of a derivative?

the slope of a tangent line at a point

  • instantaneous ROC at a point

2
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Limit of A Difference Quotient

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3
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When does a derivative not exist?

  1. When f(x) is not continuous (hole, VA, jump)

  2. Sharp Turn/Cusp

  3. Vertical Tangent

<ol><li><p>When f(x) is not continuous (hole, VA, jump)</p></li><li><p>Sharp Turn/Cusp </p></li><li><p>Vertical Tangent </p></li></ol><p></p>
4
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Connect Differentiability and Continuity

If f(x) is differentiable, then it HAS to be continuous

  • not the other way around

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Implicit Differentiation

  1. Take the derivative of each term & every time you take the derivative of y, add dy/dx

  2. Move dy/dx terms to one side, and then the rest on the other

  3. Factor out the dy/dx term to create a singular term

  4. Solve for dy/dx

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Derivative of an Inverse Function

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Slope of A Tangent Line

f’(a)(x-a)+f(a)