Taylor Rodriguez : Blog 2

This week we covered one major point of chapter two. This is the point that I will summarize in this week’s blog.
There are two formulas which need to be memorized
(((& means delta)
• The first formula is
f(x+&x)- f(x)/&x
This is the formula for a derivative. This formula is known as the secant line formula.

• The second formula is only a tiny bit different from the first

Lim f(x+&x)- f(x)/&x
&x -> 0

This formula is known as the slope of a tangent line

Solving for the problems we’ve had thus far in chapter 2 have consisted of plugging into these formulas and solving.

When given an equation you must plug x+&x into all x’s of the given equation and fill in the rest of the formula by placing – f(given equation exactly how its given)/ &x

Ex:
Find the slope of the graph of f(x)= 2x-3 at (2,1)

First you would plug in:

f(x) 2(x+&x)-3-(2x-3)/ &x
&x-> 0

Expand:

2x+2&x – 3 – 2x + 3 / &x

Take out what cancels:
2x + 2&x -3 -2x +3/&x

And you’re left with:
2&x/&x

Simplify:

2 &x/ &x
Therefore the answer is 2

((because there are no x’s left in the equation you can ignore the point (2,1) however if there had been any x’s you would have also plugged in 2 for the x’s before you simplified then solved as normal.))

There are a few helpful hints that need to be remembered
**remember that for each of these formulas any variable can be used for delta x
** remember that slope of the tangent line means to use the derivative formula
** there are many was to ask for a derivative these ways are:
Dy/dx
Y^1
F’(x)
d/dx {f(x)}
Dx[y]
D/dx