If f(2) = 3 and f'(2) = 5 find the equation of the tangent line and normal line at x = 2.
f' = the derivative
Well, what a derivative does is tell you what the slope of a tangent line is equal to at a given point on a curve. So, at the point F(2), the value of Y is equal to 3. You know that already. From the derivative, you know that at when F(2), or X=2, the slope of the line is equal to 5. So you have F(x) = 5x-7 for your tangent line at x=2. At x=2, 5(2)-7=10-7=3, or F(2) = 3.
A normal line is the negative inverse of a tangent line.
I didn't really understand it in Calc 1 (2? Don't remember if they were in that or not) either. But once you get to Calc 3, and you start using vectors and 3 dimensions, it is used alllllll the time. It's really annoying, I hate fucking normal lines.
I had Calc AB and BC in high school, but it's different in College in the States. Calc AB = Calc 1, Calc BC = Calc 2, and they are much much harder. I wished I would have paid more attention to Calc 2 in high school. Then you have Calc 3 which is multivariable calculus, basically like triple integrals over 3 dimensional space, 3 dimensional vectors, so on. And Calc 4, which is differential equations, you might have done some basic ones already in school, I don't remember. I have that next semester.
I think that is as far as they go for Calc numbers, at least at my school. After that you get into more advanced stuff.