Author Archives: hangtime

Inflection Points, Concavity & Second Derivative Test

These follow a very similar process to finding maxima and minima, except instead of setting the first derivative to zero and solving, to find inflection points you set the second derivative equal to zero. Why would you want to do this? Because they'll make you do it. But what are they? Watch and find out!

This video appears on the page: Inflection Points & Curve Sketching

Inflection Points & Curve Sketching
Inflection Points, Concavity & Second Derivative Test
Curve Sketching Examples
Sketching Parent Graphs from Derivative Graphs
Review: Vertical Asymptotes & Holes
Review: Using Limits To Find Horizontal Asymptotes
Review: Slant Asymptotes (a.k.a. Oblique Asymptotes)
Review: Relative Maxima & Minima
Review: Finding X and Y Intercepts

This chapter introduces concavity, points of inflection and the second derivative test, then reviews asymptotes, relative extrema, and how to find intercepts so you'll have the tools for graphing functions calculus-style.

Part of the course(s): ,Test Image Problem ,Calculus

Optimization Word Problems

The "other" type of derivative word problem (related rates are the big one). The way to spot these is that they'll always ask you to "maximize" or "minimize" something: the area of a rectangle, the volume of a box, the profit of a random company... No matter what the situation, the process is always the same: write down a formula and find the maxima or minima.

This video appears on the page: Optimization Problems

Optimization Word Problems
Projectile Word Problems
Maximizing Area Word Problems
Maximizing Volume Word Problems
Optimization Word Problems: Fool Proof Step by Step

The "other" derivative word problems (related rates are the big one), where you maximize or minimize the area, volume, or cost of some quantity.

Part of the course(s): ,Test Image Problem ,Calculus

Maxima, Minima, &
"The First Derivative Test"
Relative Maxima & Minima: First derivative Test
Relative versus Absolute
Relative Maxima & Minima:Easy and Hard Examples
Absolute Extrema

Extrema (maximums and minimums) come in two flavors: relative and absolute. This chapter covers both, and how to find them using the first derivative test.

Part of the course(s): ,Test Image Problem ,Calculus

Absolute Extrema

These "absolute" problems start the same way as the "relative" ones: finding critical points and then using the first derivative test to figure out whether they're maxima or minima. But then we have to test the endpoints of the interval (there's always an interval in this type of problem).

This video appears on the page: Maxima & Minima

Relative Maxima & Minima

In this video I start off explaining the difference between relative and absolute extrema. Then we get into the nuts and bolts of how to find relative extrema (maximums and minimums) using the first derivative test, and how not to get burned by common trick questions.

This video appears on the page: Maxima & Minima ,Inflection Points & Curve Sketching

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!

This video appears on the page: Graphing Derivatives

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.

This video appears on the page: Graphing Derivatives

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.

This video appears on the page: Graphing Derivatives

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.

This video appears on the page: Graphing Derivatives

Graphing Derivatives
Derivatives Graphing Overview
Sketching Derivatives Of Functions
How To Find Critical Values
Intervals Of Increase & Decrease

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).

Part of the course(s): ,Test Image Problem ,Calculus

Rolle's Theorem

Rolle's Theorem is just a special case of the Mean Value theorem, when the derivative happens to be zero. The one problem that every teacher asks about this theorem is slightly different than the one they always ask about the MVT, but the result is the same: you totally know what's going to be on the test!

This video appears on the page: Mean Value & Rolle’s Theorem

The Mean Value Theorem

In theory (and maybe in your teacher's lectures), the MVT is a Very Important Theorem all about instantaneous rate of change vs average rate of change, a theorem which underlies the very foundations of Calculus. But you don't care about that. You care about the one type of problem that every teacher puts on the test, and how to get it right!

This video appears on the page: Mean Value & Rolle’s Theorem

Mean Value & Rolle's Theorem
Instantaneous Rate of Change
Average Rate of Change

In this chapter we cover these two straightforward (but basically useless) problem types that every teacher seems to ask.

Part of the course(s): ,Test Image Problem ,Calculus

Volume Related Rates Problems (AP level)

More hard problems, this time with the theme of volume: helium balloon leaking helium (hint: negative rate); yet another ice cream cone example; and a cool modern art museum example with concrete molds.

This video appears on the page: Related Rates

Area Related Rates Problems (AP level)

This video is pretty long too, but it only covers three problems because they're pretty tough. We'll explore an oil slick spreading across a floor, an ice cream cone filling with hot fudge, and a wacky 30-60-90 sundial.

This video appears on the page: Related Rates

Triangle-Based Word Problems

Approximately half of related word problems seem to involve triangles in one form or another, either requiring the Pythagorean Theorem, special triangles, or SohCahToa. Sorry this video is so long, but we've got a lot of nuance to cover: planes and radar; roller derby teams colliding; ladders sliding down UPS trucks; and a similar triangles problem where a dude is chasing his own shadow!

This video appears on the page: Related Rates

Basic Related Rates Problems

When it comes to related rates, there aren't really any "basic" ones; this is the hardest topic in derivatives. But these problems are at least pretty straightforward: if you need to use the area formula for a circle, the words "area" and "circle" are going to be in the problem. That might not sound like much, but it's a lot more of a hint than they'll give you in the hard ones of the later videos.

This video appears on the page: Related Rates

What The Heck Are Related Rates? (free)

If you haven't watched a lot of my other videos, this one might come as a bit of a surprise. But as someone who's tutored a LOT of related rates, I know the one thing that almost every student is confused by, so I'm going to take almost the full length of this first video to drill it into your brain. You're welcome! :)

This video appears on the page: Related Rates ,free videos edit ,Free Sample Videos ,calculus free videos