Lindsey's Reflection

this week we had our first big test that covered things like limits, vertical aysmptotes and things like that.

after we moved on from that first chapter we started on the second one
.
we learned some concepts of derivatives.

we learned that a secant line is one that touches at two points while a tangent line only touches down at one point.

the formula for a secant line is this

m= f(c+deltax)- f(c)/ deltax

this is the secant slope

lim f(x+deltax)/deltax
deltax-->0

these are the things you plug into

there are many keywords to look for when finding dervatives
such as y^1, f^1(x), dy/dx, d/dx, dx[y]
slope of a tan line, slope of the curve at a point.

these are just some of the things to look for when finding a dervative

here is an example for finding a dervative that was
done in class

find the slope of f(x)= 2x-3
at (2,1)

you plug in the formula that was early shown

lim 2(x+deltax)-3-(2x-3)/deltax
deltax-->0


the three main steps to remember in doing this is

expand
cancel and factor out

after expanding you are left with this

2x+2deltax-3-2x+3/deltax

2deltax/deltax

the deltaxs cancel and the answer to this problem is 2

this concept is not too hard.

there is just a lot of work and you have to make sure you do not make a liitle mistake because
it could ruin the whole problem.