Reflection

This week in calculus we got a lot of work done. We finished Chapter 1 and took the test for Chapter 1, also we started on Chapter 2. In Chapter 2 we are learning about derivatives which is in section 2.1. To know how to find a derivative the directions will read find: y', f'(x), dy/dx, d/dx, Dx[y], slope of a tangent line, or slope of the curve at a point. To solve for a derivative, you are using the formula for the slope of a secant line: m = f(c+*x)-f(c)/*x ( * stands for the triangle symbol before x), but when you put a limit in front:
lim f(x+*x)-f(x)/*x
0
it then becomes a derivative.

EXAMPLE:
f(x) = x^2+x-3
First plug into formula:
lim (x+*x)^2 + (x+*x) - 3 - (x^2+x-3) / *x
*x>0
Next you expand:
= x^2 + 2x*x + *x^2 + x + *x - 3 - x^2 - x + 3 / *x
Then you cancel:
x^2, -x^2, 3, and -3 all cancel out
After canceling you factor:
= 2x*x + *x^2 + *x / *x
Finally solve:
= 2x + *x + 1
Final answer is 2x + 1