11/10/2015 Perkins AP Calculus AB Day 1 Section 2.1.

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Presentation transcript:

11/10/2015 Perkins AP Calculus AB Day 1 Section 2.1

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

1.Find using the definition of the derivative.

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

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

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

Perkins AP Calculus AB Day 1 Section 2.1

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

1.Find using the definition of the derivative.

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

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

4.Find any values where is not differentiable.