Modeling and Optimization
1. Understand the Problem
2. Develop a Mathematical Model of the Problem
3. Graph the Function
4. Identify the Critical Points and Endpoints
5. Solve the Mathematical Model
6. Interpret the Solution
If you follow these simple steps, you will be able find what the question is asking for.
Ex) The ladder is set 5 ft away from the wall, the ladder is 15 ft long. It starts to fall away from the wall at a rate of 1.75 ft/sec. What is the rate of the ladder falling away from the wall after 3 seconds?
1. Understand the Problem
2. Develop a Mathematical Model of the Problem
3. Graph the Function
4. Identify the Critical Points and Endpoints
5. Solve the Mathematical Model
6. Interpret the Solution
If you follow these simple steps, you will be able find what the question is asking for.
Ex) The ladder is set 5 ft away from the wall, the ladder is 15 ft long. It starts to fall away from the wall at a rate of 1.75 ft/sec. What is the rate of the ladder falling away from the wall after 3 seconds?
Notice how we drew a picture to help us in the process of finding out what we need to find. Then we made a little chart of "Changing" and "Not Changing" to show what we will be working with. The next step is to implicitly differentiate the problem with respect to "t". We are then able to apply the different values with the variables and the rate to find the final answer. It might be a long, hard, challenging problem, but if you have a little assistance and break it up into sections with good organization, you will be able to see that it is not that complicated.
One step at a time!
One step at a time!
Another example:
A police car is approaching an intersection chasing a speeding car that has already turned a corner and is headed East. When the police car is 0.6 miles NORTH of the intersection, and the speeding car is 0.8 miles EAST, the distance between them is changing at 20mph. If the police car is going 60mph, how fast is the other car going?
A police car is approaching an intersection chasing a speeding car that has already turned a corner and is headed East. When the police car is 0.6 miles NORTH of the intersection, and the speeding car is 0.8 miles EAST, the distance between them is changing at 20mph. If the police car is going 60mph, how fast is the other car going?
Again, draw a picture and find what we already know.
It really helps to draw a picture, I understand the process and what we need to do (follow the steps) but sometimes it is hard for me to find what's next on my own. When we go over the problems together, I feel so confident and everything makes sense, but when I do the problems by myself, I find the information but then I get stuck on how to apply the information to different equations.
I need my hand to be held through these problems but pretty much draw a picture, find what you know, implicit differentiation in respect to "t", insert known values, then BAM, there's the answer.
It really helps to draw a picture, I understand the process and what we need to do (follow the steps) but sometimes it is hard for me to find what's next on my own. When we go over the problems together, I feel so confident and everything makes sense, but when I do the problems by myself, I find the information but then I get stuck on how to apply the information to different equations.
I need my hand to be held through these problems but pretty much draw a picture, find what you know, implicit differentiation in respect to "t", insert known values, then BAM, there's the answer.
On another note,
Mr. Cresswell is back!
Mr. Cresswell is back!
Doesn't he look so happy?!