The first derivative gives you the formula for the slope of the tangent line to the curve at a given point.
Find the first derivative of the function y=5x/x-2:
(x-2)(5) - (5x)(1)
dy/dx = ------------------------
(x-2)^2
simplify the algebra here.
(3-2)(5) - (15)(1)
Then, at the point (3,15), dy/dx = -------------------------- = -10
(3-2)^2
What is the equation of the tangent line? In other words, what is the eqn of the tan line to the given curve at when x = 3, if the slope is -10?
y-15 = -10(x-3)
This can be re-written in other forms if desired.
