Question

Find all values of x at which the tangent
line to the graph of
y = x^2/(x + 3)

is horizontal.

Answer 1

For Horizontal
\[\frac{dy}{dx} = 0 \]
\[\frac{2x(x+3)- x^2*1}{(x+3)^2} = 0\]
\[2x^2 - x^2 + 6x = 0\]
\[x^2 + 6x= 0\]
\[x(x + 6) = 0 \]
\[x = 0,-6\]
At x = 0 , -6 y must be 0 and \(\frac{36}{-3}\) respectively .
Hence our ordered pairs are (0,0) and \((-6, -12)\)