Hello Calc
These past few days we have tested a lot learned a lot and died on the inside a lot. We learned three new main ideas / topics / formulas. We learned Rolle’s theorem, mean value theorem and optimization.
What I understand is Rolle’s theorem and the Mean Value theorem. So ill just explain the mean value theorem.
Explanation: Mean Value is if (f) is continuous on the closed interval (a,b) and differentiable on the open interval (a,b)then and only then a number c exist in (a,b)
F’(c) =f(b)-f(a)/b-a now take derivative and set equal to (a) and (b)’s slope.
So for example: F(x) =x^4-2x^2 on [-2,2] find f’(c ) =0
Is it continuous: YESIs it differentiable:YES
F(-2)=(-2)^4-2(-2)^2=8___f(2)=(2)^4-2(2)^2=8____f(-2)=f(2)=8
4x^3-4x=0-----4x(x^2 -1)=0 -----x=0,1,-1-----c= 0,1,-1
And now your done.
But what I really have problems with is optimization… What is optimization? How to do optimization? Where to start optimization? I don’t really understand it I look in my notebook look at the problems we did but I still don’t get it so if anyone can help me understand optimization please do cause confused.
That’s my biggest problem so give me ya’z wordz or wisdomz because I need all the help I can get and we had homework this weekend and I didn’t know we had homework so I didn’t do my homework so now I don’t know what will happen.
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optimization steps:
ReplyDelete1. identify all given quantities
2. write a primary equation for quantity that is to be maximized/minimized
3. reduce the primary equation to one having a single independent variable. (involves the use of secondary equations)
4. Determine the feasible domain of the primary equation (determine values for which the stated problem makes sense)
5. Determine the desired max/min value.
These can be found on the first page of your opimization packet :)
To give optimization steps in a more...non-math way:
ReplyDelete1. identify your primary and secondary equation: if it asks you to minimize the area of the rectangle with perimeter of 25465 ft, the area formula is the primary, the perimeter formula is the secondary. (I like to box off the primary)
2. if the primary equation is not in terms of one variable...like f(x) = x+2 (see how theres only one x on that side?) then you need to solve your secondary equation for a variable and plug it into the primary.
3. after simplifying the new primary equation (the one with the plugged in value), you should have it in terms of one variable now. now you can take the derivative and set equal to 0.
4. take the value you get and plug it into the secondary to get the other variable. you now have your two variables solved for.
5. if in step 4 you got two answers for the x, you plug in both of them into the secondary and look for the smallest number (if you are minimizing) or the biggest number (for maximizing).