Post Number Eleven

Wowww I just did my whole blog but when I clicked publish post there was a conflicting error and it deleted the whole thing. Here I go againnnnnnnnnnn

This week in Calculus we learned linearization. The first thing you need to know about this is the word approximate. Any time you see this word know that it is a linearization problem. The formula for linearization is f(x) = f(c) + f(c ) (x – c). Differential means when something is solved for dy or dx.

Example:
Approximate the tangent line to y = x^2 at x=1.
Dy/dx = 2x ** derivative
y = (1)^2 = 1 ** plug in x into original
dy/dx = 2 ** plug in x into derivative
f(x) = 1 + 2 (x – 1)
Fairly simple right?

Another example is
Use differentials to approximate the square root of 16.5
1. Identify an equation: f(x) = square root of x
2. f(x) + f’(x)dx: square root of x + (1)/2(square root of x)(dx)
3. Determine dx: (decimal and what follows) .5
4. Determine x: (before the decimal) 16
5. Plug in: square root of 16 + (1)/2(square root of 16)(.5)
=4.0625
Error = .0005

I thought I understood linearization when we learned it in class and when I went home and did the homework, but now I am starting to second guess myself.

One thing I am completely comfortable with is horizontal tangents:
Determine all values of x, if any, at which the graph of the function has a horizontal tangent.
y = x^3 + 12x^2 + 5
All you have to do is take the derivative and set it equal to zero, then solve for x.
3x^2
3x^2 + 24x = 0
3x( x + 8) = 0
X = 0, x = -8

One thing I am not completely comfortable with is related rates. I understand how to work the problems where everything is point blank given but I have the most trouble with the recognizing what is what inside the word problem. If anyone knows how to help with this it’d be greatly appreciated.

Also, angles of elevation have blown my mind. I need serious help with this if anyone wishes to.
The most trouble I find I am having is knowing what is given to me and what to classify it as. I know all the steps to all the types of problem and can work them once I recognize what is what, it’s just getting to that point that confuses me. I don’t know if anyone can help me with this, I know it takes a lot of practice it just is so frustrating!