Basic Differentiation Rules Rates of Change Section 2

Basic Differentiation Rules & Rates of Change Section 2. 2 AP Calc

Thm 2. 2 The Constant Rule The derivative of a constant function is 0. That is if c is a real number, then

Thm 2. 3 The Power Rule If n is a rational number, then the function is differentiable and For f to be differentiable at x=0, n must be a number such that is defined on an open interval containing 0.

Find the slope of the graph at the indicated points. Confirm your answer with your calculator. (2, 3/5) (0, 3) (-1, 12/5) Find the equations of the tangent lines that go through the given 3 points.

Thm 2. 4 The Constant Multiple Rule If f is a differentiable function and c is a real number, then is also differentiable and

Thm 2. 5 The Sum & Difference Rules The sum (or difference) of two differentiable functions is differentiable and is the sum (or difference) of their derivatives

Thm 2. 6 Derivatives of Sine & Cosine

position function- A function s that gives the position of an object as a function of time t. s(t) Rate = Average velocity=

Find the average rate of change of the function over the indicated interval. Compare with the instantaneous rate of change at the endpoints. f(t)=t²-3 [2, 2. 1]

The velocity function is the derivative of the position function

The position of a free-falling object under the influence of gravity:

A ball is thrown straight down from the top of a 220 foot building with an initial velocity of -22 ft/sec. What is the velocity after 3 seconds? What is the velocity after falling 108 feet?