Academic Detention Blog #1

I always forget how to find the equation of a tangent line, but it is so simple. So, I thought I would discuss the steps.

Finding an equation of a tangent line:

Steps:
1. if no y, plug in x to original problem
2. take derivative
3. plug in x (gives your slope)
4. write in point slope form

Example:
y=sin2x at x= pi/2

1. y=sin2(pi/2)=sin(pi)= 0 (pi/2, 0)
2. y^1=cos(2x)(2) *(y^1 is y prime)
2cos(2x)
3. 2cos(2(pi/2)=2cospi= -2
4. y-0=-2(x-(pi/2))

If they ask you for the normal line, it is the same steps except your slope would be perpendicular.


My question is about instantaneous speed. Do I just plug into the formula
lim f(x+h)-f(x)/h ?
h-->0