Calculus Problem?

Question

Find the equation of the line tangent to the curve y=x+(1/x) at the point (5,26/5)

Answer 1

First we find the derivative of the curve at the point, which is 1-1/x² evaluated at 5, which is 24/25. This is the slope of the tangent line. To find the line itself, we plug this information into the point-slope form to obtain:

y-y₀=m(x-x₀)
y-26/5 = 24/25 (x-5)
y-26/5 = 24x/25 - 24/5
y = 24x/25 + 2/5

And we are done.