The Constant Rule m = 0 The derivative of a constant function is 0.

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Presentation transcript:

The Constant Rule m = 0 The derivative of a constant function is 0. I don’t even have to think too hard to do that. m = 0 The derivative of a constant function is 0.

The Power Rule That was easy If n is a rational number, then the function f(x) = xn is differentiable. That was easy

The Constant Multiple Rule If f is a differentiable function and c is a real number, cf is also differentiable. These are the easy ones. Let’s try some more difficult problems. I knew that was coming.

Constant Multiple Examples

Homework Page 115: 25 – 30 All

Sum and Difference Rule The derivative of the sum, or difference, of two differentiable functions is differentiable and is the sum, or difference of their derivatives.

Derivative of Sine and Cosine

Sine and Cosine Examples

Homework Page 115: 4 – 24 Even Numbers

Finding an Equation of a Tangent Line Find an equation of the tangent line to the graph of f(x) = x2 when x = –1 f(x) = x2 First find the point of tangency at x = -1 The point of tangency is Next, find the derivative of f(x) = x2 y = -2x - 1 Therefore, the slope of the tangent line at x = –1 is We now have a point on the line and the slope, so use the point-slope form to find the equation of the tangent line.

Graphs of Derivatives Since f is cubic, f’ is quadratic. Compare the graph of the following function with the graph of it’s derivative. Since f is cubic, f’ is quadratic. f increases, f’ is positive. Let’s look at another example. f decreases, f’ is negative. f increases, f’ is positive. I think I can see the pattern.

Graph of Sine and its Derivative Increasing Decreasing Negative Negative Positive Increasing Decreasing Positive I get the picture. This is pretty easy.

Comparing a Function and its Derivative In each of the following, determine which is the function, f and which is the derivative, f’, and explain your answer. f f f f’ f’ f’ f is quadratic f’ is linear f is cubic f’ is quadratic f is linear f’ is constant When f decreases f’ is negative f constantly decreases f’ is always negative f constantly increases f’ is always positive When f increases f’ is positive That was easy

Graphs of Derivatives Worksheet Homework Graphs of Derivatives Worksheet