I almost forgot about the blog again! The holidays are throwing me off. I never know what day it is haha. Alright well here we go again..
MAX or MIN
First we need the steps:
1. First Derivative Test
2. Plug critical values into ORIGINAL function to get Y-values
3. Plug endpoints into ORIGINAL function to get Y-values
4. Highest Y-value is absolute max and lowest Y-value is absolute min
Next we can do an example problem:
f(x) = 2(x)^4 - 4(x)^3 on [0,5]
8(x)^3 - 8(x)^2
8x^2[(x)^2-1]
Set equal to zero to get x = 0,-1,1
Using 0, -1, 1 and the point in the problem, plug ALL values in for x.
smallest is the min and largest is the max
MIN [1,-2] and MAX [5,750]
*Remember absolute max and mins are written as a point or just the y-value.
I also want to point out that taking the tangent line is so easy. I don't know why I always forget it. It is simply take derivative, plug in x-value into derivative, and then put into point slope form. Simple? Yeah I know..now.
Now I'm putting the steps for optimization because I STILL don't understand it! I just don't know what my problem is with optimization..I can know the steps or formulas but still fail miserably at the problem.
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.
Any advice for this? Thank youuuuu :)
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Steps for optimization:
ReplyDelete1. Read each problem slowly and carefully. Read the problem at least three times before trying to solve it. Sometimes words are tricky and unimportant. Find out exactly what the problem is asking. If you misread the problem or hurry through it, you have NO chance of solving it correctly (coming from my experience...).
2. If appropriate, draw a sketch or diagram of the problem to be solved. Pictures are a great help in organizing and sorting out your thoughts.
3. Define variables to be used and carefully label your picture or diagram with these variables.
4. Write down all equations which are related to your problem or diagram. Clearly label the equation which you are asked to maximize or minimize. In most problems, you are given an equation that you're optimizing and an equation that you solve for one variable.
Before differentiating, make sure that the optimization equation is a function of only one variable.