Question

Find an equation of the tangent line to the graph y at the point x.

y = 3x/(2x + x^-1) at x=1

Answer 1

First you find the derivative of the function:
y'=6x/(2x^2+1)^2
Check the value at x=1
y'(1)=2/3
the function has value at x=1
y(1)=1
So slope is 2/3 and takes the point 1,1
y=2/3x+1/3