question #6\nthe graph of f(x) = 1/3x³ - 2x² + 3x is shown below. use the graph to determine the interval of…

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

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

Answer

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 $x_1<x_2$, we have $f(x_1)>f(x_2)$. 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. $(1,3)$