`f(x) = x + 4/x, (-4, -5)` Find an equation of the tangent line to the graph of f at the given point.

Expert Answers
hkj1385 eNotes educator| Certified Educator

The given function is:-

f(x) = x + (4/x)

differentiating both sides w.r.t 'x' we get

f'(x) = 1 - {4/(x^2)}

Now, slope of the tangent at the point (-4,-5) = f'(-4) = 1 - (1/4) = 3/4

Thus, equation of the tangent at the point (-4,-5) and having slope = 3/4 is :-

y - (-5) = (3/4)*(x - (-4))

or, 4y + 20 = 3x + 12

or, 4y - 3x + 8 = 0 is the equation of the tangent to the  given curve at (-4,-5)