This was the final week of school of 2014 and it went out with a bang with the way we were able to conclude with chapter four.After chapter four we had a quiz on the chapter along with the previous topics we discussed such as limits and derivatives.I had some trouble with finding the critical points and the other information we had learned in the last chapter about graphing.However,I was able to solve this problem by remembering how to do problems such as these with a trick.So for local max/mins,you in the numbers you found in the 1st derivative(critical numbers) to the second derivative to find the local max or min.For a local max if the value of the second derivative is less than zero then it is a local max and if the value of the second derivative is greater than zero it is a local min.In a special case where the value of the second derivative equals zero then anything is possible.
This week was primarily focused on reviewing Chapter 4,which I have found to be one of the most challenging units we have had so far but now I have grasped the concept a little better.The modeling and optimization was simply figure out the the lengths of the sides,plug it into a formula,solve that formula for one variable and plug that variable into a formula you are given to solve it.After all of this you take the derivative and set the equation where you solve for the value.When you solve for the value,you plug in the number into the original equation.
The related rates I thought related rates were much more difficult than optimization.While it combined the analytical problem solving in optimization,it also had the additional piece of information such as the volume and side changing with respect to time.A way I then began remembering in order to solve a problem such as those were to first identify the variables,develop a model of the problem,write an equation relating the rate of change being looked for to the variable which is being seeked
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