Post #21

Since I been having trouble remembering linearization, I'll explain that.

The key word in linearization is approximate. Also, if there is a decimal in the problem, its another hint that you will be doing linearization.

The steps of linearization are

1. Identify and equation

2. f(x)+f'(x) dx

3. Determine dx (the decimal)

4. Determine x (the whole number)

5. Plug in

Examples:

Use differentials to approximate the square root of 16.5.

1. The equation would be f(x) = the square root of x

2. Take the derivative of f(x) which we found to be the square root of x

x^1/2 = 1/2 x^-1/2 dx or 1/2 square root of x dx

Then at f(x) and f'(x): the square root of x + 1/2 square root of x dx

3. dx = .5

4. x = 16

5. Plug in: the square root of 16 + 1/2 the square root of 16 (.5)

4+1/((2)(4) (.5) = 4 + 1/8 (.5) = 4.0625

The example we been seeing on the practice AP is

If f(1)=2 and f'(1)=5, use the equation of the line tangent to the graph of f at x=1 to approximate f(1.2).

For this problem, all you have to do is find the equation of the tangent line then plug in 1.2 for x.

To find the equation of a tangent line, you need a point and a slope.

You are given that f(1)=2 so your x is 1 and your y is 2 (1,2) is your point.

Then they give you that f'(1)=5 so your derivative (slope) is 5.

Now plug in: y-2=5(x-1)

Next plug in 1.2 for x

y-2=5(1.2-1)

y-2=5(.2)

y=1+2 = 3

I can use help on related rate problems because I get confused about what is given and what is not. Also, I need to learn how to work my calculator for the calculator portion. Other than that, I think I just need to study big time tonight because I am quite terrified for tomorrow.