11th post

This week in calculus we learned linearization and mrs. robinson made us write down our top five things we did not understand so far in calculus. She then took the major problems we were having and made a packet out of them so we could practice for the test on wednesday.

I finally have a grip on the horizontal tangent problems. First you take the derivative of the function and set it equal to zero and solve for your x values. Whatever you get for x is your values that have horizontal tangents.

What i understand the most out of all we have learned so far is related rates.. i feel very comfortable working these problems. let's look at an example of one.

They tell you that the radius of a right circular cylinder is [the square root of(3t+5)] and that the height is t^7. They want you to find the rate of change of the volume of the cylinder.

1. The first step is figuring out the formula for the volume of a right circular cylinder which is V= (pie) r^2h.
2. Next plug in what you are given V= (pie) (the square root of 3t+5)^2 (t^7)

Also note that the square root will cancel because it is being raised to the second power.

So now we are left with V= (pie) (3t+5) (t^7)

3. Now distribute the t^7 with the 3t+5 to give you:
V= (pie) (3t^8 +5t^7)

4. Now take the derivative of the function:
dV/dt= (pie) (24t^7 + 35 t^6)

5. Now you can take out a t^6

6. The answer will be dV/dt= (pie) (t^6) (35 + 24t)

What i still do not understand is angle of elevation. I still do not understand what i am looking for and how to find it. I know it is like related rates at one point but i do not understand how to get to that point. Another point i am confused on is linearization. I do not quite grasp the concept of it and where and how it is used. If anyone can help with these problems i would greatly appreciate it. Good luck to everyone on the test this week :)