alright, this week we studied for our test, and we did our packets; however, last week I didn't know how to do optimization, so I am going to explain that and other stuff that I know.
EVT: the EVT states that a continuous function on a close interval [a,b], must have both a minimum and a maximum on the interval. However, the max and min can occur at the endpoints.
Rolles theorem gives the conditions that guarantee the existance of an extrema in the interior of a closed inteval.
Rolles: Let f be continuous on a closed interval [a,b] and differentiable on the open interval (a,b). If f(a)= f(b) then there is at least one number, “c” in (a,b) such the f '(c)=0
MVT: If f is continuous on the closed interval [a,b] and differentiable on the interval (a,b) then there exists a number c in (a,b) such that f '(c)= (f(b)-f(a))/(b-a).
Steps for optimization
1.Identify primary and secondary equations. The primary will be the one you are maximizing or minimizing, and the secondary will be the other one.
2.Solve secondary equation for one variable, and plug into the primary. (if the primary only has one variable, this step is not necessary.)
3.Take the derivative of the primary, and set it equal to zero; solve for x.
4.Plug into secondary equation to find the other value, check end points if necessary.
Something I don't understand is the tangent line stuff, I do not even know how to start a question that asks about that. And it's all over the packets we just got!
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Tangent Line - you take the derivative and then when they give you a point you plug in the x im pretty sure.
ReplyDeleteyea like ryan said take the derivative. then plug in the x from the point given into the derivative you just got. This gives you your slope. Then plug the point given and the slope you just got into slope intercept form which is y-y1=slope(x-x1)
ReplyDeleteMher,
ReplyDeletetangent line is really easy once you know how to do it. You are given a function and a point. First just plug in the point into the x's of the function. That gives you your y value. Then take the derivative of the function. After taking the derivative plug in the point given and that gives you your slope. You then end up with a point and a slope, so of course you put that into pointslope form which is y - y1 = m(x - x1)
first you take the derivative of the function given, then after that you plug in your x-values from the point that was given, this will give you your slope. then you take the point that was given, and your slope and you plug it into slope-intercept form. y-y1=m(x-x1)
ReplyDeletethen thats your answer, really it's a lot easier than it looks
tangent line is simple.
ReplyDeletetake the derivative of the function and plug in the x you have.
get a point...now use point-slope form with the slope it asks you to use.
you have a function and a point so plug in the point to get the y value then do the derivative then plug in that point to find the slope.
ReplyDeleteOk, so if you start off with a function and an x value, you plug in your x value into the origional function to get your y value. After this you'll have an x and y value for the equation. To find your slope take the derivative of the function and plug your x value in. Once you have all of these things, you are to plug them into point-slope form.
ReplyDelete