Find the equation of the tangent line to the graph of the function f(x)=x+3/x−4 at the point (0,−3/4)

Question

Find the equation of the tangent line to the graph of the function f(x)=x+3/x−4 at the point (0,−3/4)

y =

Answer 1

If you are talking about:

In order to find the tangent line, you need the slope. To find the slope, you can take the derivative. To take the derivative, you would use the quotient rule which is:

(u/v)' = (u'v - uv')/v²

In this case, u = x + 3 and u' = 1 while v = x - 4 and v' = 1 therefore

f '(x) = [(1)(x - 4) - (x + 3)(1)]/(x - 4)²

f '(x) = (x - 4 - x - 3)/(x - 4)²

f '(x) = -7/(x - 4)²

So f '(0) = -7/(-4)² = -7/16

Using the point-slope of a line (y - y₁) = m(x - x₁) we can plug in the point (0, -3/4) to get:

y - -3/4 = -7/16(x - 0)

y + 3/4 = -7/16x

y = -7/16x - 3/4