Now on the question at hand. First, some quick references for you. The first derivative of the function f(x), is the slope of the tangent line to the function at the point x:**If the first derivative f' is positive, then the function f is increasing (pointing upwards)If the first derivative f' is negative, then the function f is decreasing (pointing downwards)**

As for the second derivate, the second derivative of a function is the derivative of the derivative of that function:

The second derivative is like the movie Inception. The first derivative tells us whether or not the function is increasing or decreasing. The second derivative shows us whether or not the first derivative is increasing or decreasing. So the second derivative plays directly off of the first.

If the second derivativeturns out to be positive, then the first derivative will be increasing. The slope of the tangent line to the function is increasing as x increases. If the second derivative turns out to be negative, then the first derivative is decreasing. The slope of the tangent line to the function is then decreasing as x increases

Here is some more in-depth information, but this should be a good start. If you would like to see it in action, take a look:

]]>

Are you getting ready to take the SAT? Have I got the book for you! Presenting *The Humongous Book of SAT Math Problems*, your one-stop show to a metric ton (give or take) of math practice for the SAT Test. The book contains all of the following, except for one. Try to figure out which is not included:

- Test-taking tips, including specific advice for multiple-choice and grid-in questions
- In-depth mathematical tutoring on all of the major topics included on the SAT
- Practice problems for all four categories of mathematical SAT questions
- The math sections of three full-length practice SAT tests
- A bronze bust of former president William Howard Taft

Set your math phasers to "excited"! Click here for ordering info.

]]>Click here to download and print the chart. Alternately, you can right-click and select "Save Image" to save it to your computer.

Note that the chart opens in a new window. If you can't see it, you may need to temporarily disable pop-up blockers.

]]>Every day Mike gets a ton of email from people practically begging to buy advertisements on his site. Actual begging. We feel sorry for these people, because what they don't know is that Mike made a (probably very short-sighted) pledge to never sell ads on the site for any reason. "But can't we just throw money at you?" they ask, usually in the form of impersonal spam. "No," Mike says. "I must hold to a promise, a sacred covenant, that I sometimes really regret making." For those of you thinking, "Sure, there's no advertising, but practically every page is an ad for Mike's books. Doesn't that count as advertising?" understand that I am staring at you with a squinty stare, telepathically asking you to kindly put a sock in it, because you're embarrassing me in front of my new friends--friends that could potentially buy the calculator I ruined by signing it with a silver Sharpie.

To help keep the site free, Mike is auctioning off this calculator, which is lightly used, but it contains all the important pieces (like connection cables, the manuals, an alternate TI-84 face plate (let your dork flag fly) and is in incredible shape. It works like a charm, as you can see by the mundane and meaningless calculations I took a picture of. In case you were wondering if this complicated piece of machinery can add, the answer is a resounding YES! (I may or may not have utilized the full power of this guy.)

]]>Are you thinking, "This must be an optimization problem, where you are asked to calculate the *bear* minimum"? If you did think that, please know that I am, as you read this sentence, smiling approvingly and giving you polite golf applause for your clever pun. However, this problem is all about definite integrals, so there is no time for joking around.

Steel yourself for the battle of your life! Attack this problem with your *bear* hands! But please, before you do, I would like the polite golf applause reciprocated.

With a nod of his head and a wink of his eye, he will promptly ask you to stop trespassing, and for Christmas this year? A restraining order from Santa.

No, this is not how you planned things at all...

]]>

Have you ever loved something so deeply, so meaningfully, so completely, so profoundly that it would really irk you if you dropped that thing into a bubbling vat of acid? I have, and so that you may learn from my tragedy, I will share a horrific tale from my past.

Once, on a whim, I spent an entire summer trying to carve a perfect cube from a piece of driftwood on the beach. Don't ask why; this is what all math teachers do during summer break, and if teachers tell you otherwise, they are lying. Look at their hands carefully—they are probably whittling as they lie to you!

Click here to read more and to attempt the Problem of the Week.

]]>