Ap calc optimization problems12/13/2023 ![]() ![]() Check the AP website at for more details on restrictions on calculators. Therefore students should become comfortable with their graphing calculators through regular use. Find the y coordinate is easy enough, all you have to do is put the one into that formula. testmakers who develop the AP calculus exam recognize that a graphing calculator is an integral part of the course. You know that the tangent line is going to go something like that. x equals 1, it's about there and we know the x coordinate of that spot is 1 but one but we don't know the y coordinate yet. But it's not really that hard to deal with. The other thing that makes it a little bit harder is, we don't have the point it goes through yet, we just have one of the co-ordinates. Looks a lot harder right? That's actually not that hard a derivative to do. Let's go and try another one that's just a little harder. That's the equation of the line that touches a curve at that spot. We've got y plus 4 equals 3x plus 3, so 3x, taking 4 from both sides, there you have it. When x is -1, y is -4, put that in and put in our slope, a little bit of simplifying and we'll have our equation. So y minus equals, I always like to do it this way because just leave blanks for what you're going to substitute in. So my guess for the slope earlier on that was not so far off. So the slope when x is -1 is 3 times -1², it's just 3. Well this slope formula only requires me to use the x number. ![]() ![]() The one that makes the equation of any line if you have the slope and one point, well the slope will be right go in a minute. Same problem we just found this formula for the slope, we know that it's going to go through this point and this is where you'll find the point slope formula. The slope over here is steeper, the slope right there, not as steep. This is a curve, the slope here is a certain number. ![]() but that is because you were dealing with straight lines. A slope that was a formula, you did a slope that WAs a single number. Now this is kind of funny ,slope equals a formula, that something you never had in algebra one. Let's see y=x³-3 so the derivative of that is 3x², the -3 is of course a constant and derivative of a constant is 0. What we're going to do is the derivative of the formula we want the line to be tangent to, and then we'll see what happens. I know I have heard this before, oh yeah derivatives. Now, how are we going to get what we need though because remember for a line you need to have a point, you got it. But we don't have to guess because we've got calculus to do this. So looking at that I think it's probably a slope of 2, 3, 4 or something like that. (-1, -4) okay there is the point of tangency and the tangent line goes something like that. So we're supposed to find the equation of a line that's tangent to that curve, and the problem tells us where it wants the tangent to be. One of them is a basic problem, the other one is just one little step harder. We're going to do two practise problems here. But we need the slope and that's where the calculus comes in. Whenever you do these problems, you're going to be told what the point to put it at. Well you've done line equations since Algebra 1, and remember what it requires you have to have a slope and you have a point. There you go, so there is the tangent line and it touches just at one spot there. The thing that makes a tangent line special is that, it touches a curve only at one spot. Applications involving optimization problems.Ī tangent line is just what it says, it's a line. We'll go on to a few practise problems and then we'll go to some applications. So we're going to begin by doing a little bit of basic review. What this topic does is help you find the minimums and maximum of curves, and you can also find lines that are a tangent to a curve at any spot. Well this is a topic from fairly early on in the year just after you learnt how to do derivatives. I think it's unlikely not knowing them would greatly impact a person's score.Tangent lines and optimization. So I might take a look at them for derivatives, but it's not something I'd stress over. The most recent example I can find is 2004 AB3 ( ), although it looks like you can get away with not knowing the actual derivative formula by using the nDeriv feature for part (a) (since they ask the derivative at a point) or by knowing the value of the inverse function's derivative at a point (a skill that is also used in 2007 AB3). However, every once in awhile, an inverse trig function will rear its ugly head on the free response. It's also still in the course description ( ) on page 15 of the PDF file (called page 9 on the page itself). I know it's not a topic that's often tested, and if it comes up, it's likely just one question on the multiple choice. I can't imagine it's on the AB test, though, since you don't learn that technique (or at least aren't required to).īut differentiation of inverse trig functions can be on the AB test still. I think integration of inverse trig functions is fair game on the BC test, because the technique required to do those is integration by parts. ![]()
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