The Derivative and Graphs
We have seen how to differentiate functions from several different families: polynomials and poly-type functions, trig and inverse trig functions, exponentials and logs, and even hyperbolic functions and their inverses. Now we can use this knowledge to help us sketch graphs of functions in general. We’ll see how the derivative helps us understand the maxima and minima of functions, and how the second derivative helps us to understand the so-called concavity of functions. All in all, we have the following agenda:
• global and local maxima and minima (that is, extrema) of functions, and how to find them using the derivative;
• Rolle’s Theorem and the Mean Value Theorem, and their ...