<p>i used to beast ap calc (ab). but now i dont understand ANYTHING</p>
<p>we're doing optimization, but i dont understand it. the practice in class problems are always easier than the homework.</p>
<p>the point of optimization is to find max and mins. Basically by setting derivatives equal to 0. There are other (somewhat) more complicated things like Lagrange Multipliers, but I doubt you’re covering that.</p>
<p>i understand that.</p>
<p>i’m talking about more complex problems. </p>
<p>and example:</p>
<p>find a rectangle with the largest area inscribed in a triangle with legs 3 and 4 if two sides of the rectangle are touching the legs.</p>
<p>in class my teacher found the equation of the line and a point… but i have no idea what to do or why he did that. ugh he doesn’t explain.</p>
<p>Well obviously the biggest rectangle would have a corner touching the hypotenuse (it’s a right triangle, right?). So then you would probably want the area of the rectangle as a function of where on the hypotenuse the corner touches.</p>
<p>Yes. But I don’t know HOW to come up with a function.</p>
<p>The (X,Y) coordinate on the hypotenuse has to be collinear with its vertexes, and what you’re trying to optimize is the product of X and Y. The two equations you need are obtained by using the slope formula between (X,Y) and (0,4), and (X,Y) and (3,0).</p>
<p>you know it has to be a right triangle given that two sides of the rectangle must touch the legs. So one vertex is the point that the legs meet at, and the opposite one (the one that is not adjacent to that one) is on the hypotenuse somewhere. That vertex’s coordinates (if the other one’s are 0,0) are the length and width of the rectangle. You want to maximize the rectangle’s area so you want to maximize the product of these two coordinates. the eq. of the line of the hypotenuse is y= 4/3(x-3) let’s say, so we want to know when yx or 4/3(x-3)x is largest (over the interval that is the hypotenuse).</p>
<p>You guys beat me to the punch… </p>
<p>Once you multiply the two together you will get a function that you can graph and find the max value. yay for math.</p>
<p>Also, just to throw this out there, there’s really no excuse for not doing Calculus BC instead of AB. You learn maybe three additional concepts that are really straightforward, and get twice as many credit hours.</p>
<p>^Except when your HS doesn’t let you take both in one shot</p>
<p>Pioneer- just to throw it out there, every school is different. If you don’t have anything pertinent to my OP then please don’t say anything</p>
<p>Thanks to all who helped.</p>