This week in Calculus we pretty much just reviewed and had a quiz. At the end of last week and the beginning of this week, I was still confused with optimization. By the time of the quiz, I finally caught on to optimization. This week we were also given studyguides to work on right up until our exam. They're pretty big, but we'll get through them.
So first I didn't understand optimization and where the equasions came from, or even how to decide which equation was to be maximized. I kept on confusing myself and going in circles with the problems. After we were given the list for optimization "in English" I understood it a lot better. It's really simple when you know what you're looking for
The steps for optimization are as follows:
1. Identify your primary and secondary equations. Primary will be the one the problem is asking you to minimize or maximize. I've also noticed that the secondary will usually be set equal to a number.
2. After finding secondary, solve it for one variable if there are two.
3. Once you have this variable, plug it into your primary equation for the variable you solved the secondary equation for
4. Take the derivative of the equation you just formulated and set it equal to zero (this zero will become one of your answers)
5. Once you come out with your zeros, plug them into your secondary equation and solve for the variable you have left (this will give you your second answer)
So far looking through the packets, I've only gotten to the limits. I don't understand how to look at a graph and find what the limit is. Can someone please explain?
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you determine what number they are asking you to look at and then from there you determine from which side of the graph to look from. if it has a minus sine then its from the left(negative)side, plus is from the right (positive) side. You look from that side what number it is approaching or discontinuity. its hard to fully explain without a graph. lol hope it helps.
ReplyDeleteits really easy, you just find the number the limit is going to..then find it on the x-axis..and look to see if it wants you to find the left or the right of the graph..then see if there is any discontinuity or if there is something there
ReplyDeleteyou find out which number you looking out then you determine which side of the graph you will be looking at. it its negative your lookin from the left and positive you lookin from the right. from there you find the discontinuity.
ReplyDeleteusually it'll have the - or + sign after the number it wants you to find the limit is approaching. so you take you fingers out (as john would say) and trace from the right and left sides and see where they are heading. That then is your limit :)
ReplyDeleteby the way this is probably no help because i have no graph to try to show this to you
determine if the limit is increasing or decreasion, looking from left to right. then try to figure out what kind of equation it is, like if it's a parabola it's gonna be an equation with x^2, then figure out what your equation would look like if you took the derivative of it. then look at your new equation and figure out what type of graph it will have, then if it's increasing or decreasing will determine whether your graph will be positive or negative.
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