Differentiation Rules (Constant, Power, Sum, Difference)

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Presentation transcript:

Differentiation Rules (Constant, Power, Sum, Difference) AP Calculus October 3, 2016 Mrs. Agnew

Essential Question Essential Vocabulary How can we find the derivative of a function quickly and efficiently? Essential Vocabulary Constant Rule Power Rule Constant Multiple Rule Sum/Difference Rule Positive-Velocity-Acceleration Problems

Basic Rules The Constant Rule: The derivative of a constant is zero. The Linear Rule: The derivative of a linear function is the slope.

The Power Rule Given f(x) = xn, then… Guided Practice… Including negative exponents, rational exponents, and radicals

Constant Multiple Rule The derivative of a constant times a function is equal to the constant times the derivative of the function. Guided Practice…

Sum & Difference Rules The use of these rules, along with the power rule, makes finding the derivative of polynomials easy.

The Second Derivative The second derivative of a function is the “derivative of the derivative.” Notations for second derivative:

P-V-A Problems Given a function that gives the position of an object at any time t, the velocity and acceleration of the object are found by: Velocity: Acceleration:

Guided Practice Find tangent lines to curves and horizontal tangent lines Find second derivatives P-V-A problems Application Problems…

Homework: Page 115 – 118 #15, 17, 35, 39 – 51 (Odd), 59, 61, 80, 87 – 92, 95, 117