Question

question #6
the graph of f(x) = 1/3x³ - 2x² + 3x is shown below. use the graph to determine the interval of decrease.
(1,3)
(-∞,1)∪(3,∞)
(3,1)
(-∞,3)∪(1,∞)

Explanation:

Step1: Recall function decrease property

A function $y = f(x)$ is decreasing on an interval if for any two points $x_1$ and $x_2$ in the interval with $x_1f(x_2)$. Visually, the graph of the function goes down - hill as we move from left - to - right.

Step2: Analyze the given graph

Looking at the graph of $y=\frac{1}{3}x^{3}-2x^{2}+3x$, we can see that the function is decreasing between $x = 1$ and $x=3$. The function has a local maximum at $x = 1$ and a local minimum at $x = 3$.

Answer:

A. $(1,3)$