Ex 4 p. 109 Finding an Equation of a Tangent Line Find the equation of the tangent line to the graph of f(x) = x 3 when x = -2 To find an equation of a line, we need a point and a slope. The point we are looking at is (-2, f(-2)). In other words, find the y-value in the original function! f(-2) = (-2) 3 = -8. So our point of tangency is (-2, -8) Next we need a slope. Find the derivative & evaluate. f ‘(x) = 3x 2 so find f ‘(-2) = 3 ٠ (-2) 2 =12 Equation: (y – (-8)) = 12(x –(-2)) So y = 12x +16 is the equation of the tangent line.
Informally, this states that constants can be factored out of the differentiation process. Ex 5 p. 110 Using the Constant Multiple Rule
Last but not least, Ex 8, p112, Derivatives of sine and cosine Function Derivative
Assign: 2.2a p. 115 #1-65 every other odd Heads up – each of you will need to create a derivative project – something that you will use to remember all the derivative rules we learn in this chapter. This will be due Monday Oct 17. See paper for details. (online too)