This chapter is a grab bag of graphical analysis. Intervals of increase and decrease, how to find critical values, how to sketch the derivative of a function just from the sketch of the original function, and a general intro to relative extrema (maxima and minima).
Derivatives Graphing Overview
Derivatives can get pretty confusing when you start to graph them: relative maxima and minima, absolute extrema, inflection points, intervals of increase and decrease, critical values... It's a lot to take in. So in this video I just quickly go through the vocab and show how it's all related, so that the later videos will make sense as we get into how to solve each type of problem and calculate these darned things.
Sketching Derivatives Of Functions
Most of this section of calculus is about difficult calculations where you have to take derivatives and do all kinds of crazy stuff to them. But at least it's mostly plug-and-chug. Sketching derivatives from the sketches of functions, though, is a really difficult topic that messes up even the best calculus students. So in this video I break it down to make it about as close to plug-and-chug as you can make it.
How To Find Critical Values
The most common critical values are the ones that are easy to find: just set the derivative to zero and solve for x. But discontinuities, asymptotes, absolute values, trig functions, and a few funky functions are also pretty common (teachers are mean!), so I cover what to do about those in this video as well.
Intervals Of Increase & Decrease
When it comes to derivatives, it's all about slope (a.k.a. "rate of change"), and "increasing" and "decreasing" are just different words for positive and negative slope. But saying it and doing it are two different things, so that's what the examples in this video are for!
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