Question

Find the equation of the tangent line
f(x) = x + (2/x); x = 4
y=?

Answer 1

when x = 4, y = 4 + (2/4) = 9/2

The tangent line requires the slope at x = 4.

The slope of f(x) is f ' (x) = 1- 2/(x^2)...quotient rule
So at x = 4, the slope is 1 - 2/16 = 7/8

So the equation of the tangent line whose slope is 7/8 and passes through (4, 9/4) is

y - (9/4) = 7/8(x - 4).