Find all points on the graph of the function $f ( x ) = \frac { x ^ { 2 } } { x + 2 }$ where the tangent line is horizontal.
A) There are none.
B) (2, 1)
C) (0, 0) and (-4, -8)
D) (0, 0)

Question

Quizplus · Accepted Answer

The tangent line is horizontal where the derivative is zero. The derivative of $f(x)$ is $\frac{d}{dx}\left(\frac{x^2}{x+2}\right)$. Setting the derivative equal to zero and solving gives the points (0, 0) and (-4, -8).

Find All Points on the Graph of the Function f(x)=x2x+2f ( x ) = \frac { x ^ { 2 } } { x + 2 }f(x)=x+2x2​

Find All Points on the Graph of the Function $f ( x ) = \frac { x ^ { 2 } } { x + 2 }$