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AP Calculus AB

AP Calculus AB. Day 1 Section 2.1. or. The Derivative (Definition of the Derivative). Gives a generic expression into which we can substitute any x to get a numeric value of the derivative at that point. The Alternative Form of the Definition of the Derivative.

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AP Calculus AB

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  1. AP Calculus AB Day 1 Section 2.1 Perkins

  2. or The Derivative (Definition of the Derivative) Gives a generic expression into which we can substitute any x to get a numeric value of the derivative at that point. The Alternative Form of the Definition of the Derivative Gives the numeric value of the derivative at a given point, x = c.

  3. Find using the definition of the derivative.

  4. 2. Find the equation of the tangent line to at (1,5). Use the alternative form of the definition of the derivative. D.S.

  5. 3. Find the slope of the tangent line to at x = 2. This function has a sharp turn at x = 2. Therefore the slope of the tangent line at x = 2 does not exist. • Functions are not differentiable at • Discontinuities • Sharp turns • Vertical tangents

  6. 4. Find any values where is not differentiable. This function has a V.A. at x = 3. Therefore the derivative at x = 3 does not exist. Theorem: If f is differentiable at x = c, then it must also be continuous at x = c.

  7. AP Calculus AB Day 1 Section 2.1 Perkins

  8. or The Derivative (Definition of the Derivative) The Alternative Form of the Definition of the Derivative

  9. Find using the definition of the derivative.

  10. 2. Find the equation of the tangent line to at (1,5). Use the alternative form of the definition of the derivative.

  11. 3. Find the slope of the tangent line to at x = 2.

  12. 4. Find any values where is not differentiable.

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