Let $f(x)=x^{-2 / 3}$ .Use a graph to decide which one of the following statements is true.
A)When x = -5, the derivative is negative; when x = 5, the derivative is positive; and as x approaches infinity, the derivative approaches 0.
B)When x = -6, the derivative is positive; when x = 6, the derivative is also positive, and as x approaches infinity, the derivative approaches 0.
C)When x = -7, the derivative is negative; when x = 7, the derivative is positive, and as x approaches infinity, the derivative approaches infinity.
D)The derivative is positive at at all values of x.

Question

Quizplus · Accepted Answer

The derivative of $f(x) = x^{-2/3}$ is negative for negative $x$ and positive for positive $x$. As $x$ approaches infinity, the derivative approaches 0.

Let f(x)=x−2/3f(x)=x^{-2 / 3}f(x)=x−2/3 Use a Graph to Decide Which One of the Following

Let $f(x)=x^{-2 / 3}$ Use a Graph to Decide Which One of the Following