- #1

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## Homework Statement

Find all x coordinates of points (x, y) on the curve y = (x − 2)

^{5}/(x − 4)

^{3}where the tangent line is horizontal

## Homework Equations

Quotient Rule - Differentiation

## The Attempt at a Solution

So I could guess, that if tangent line is horizontal, the equation of tangent line to curve is y = c, where gradient is 0.

So, first derivative of the curve is suppose equal to zero.

dy/dx;

0 = ((5)(x - 2)

^{4}(1)(x - 4)

^{3}- (x - 2)

^{5}(3)(x - 4)

^{2}(1)) / ((x - 4)

^{3})

^{2}

0 = (5(x - 2)

^{4}(x - 4)

^{3}- 3(x - 2)

^{5}(x - 4)

^{2}) / (x - 4)

^{6}

Okay now I'm stuck.