determining a local maximum and minimum\nanalyze the table of values for the continuous function, f(x), to…
determining a local maximum and minimum\nanalyze the table of values for the continuous function, f(x), to complete the statements.\na local maximum occurs over the interval \na local minimum occurs over the interval \nx f(x)\n-3 -16\n-2 -1\n-1 2\n0 -1\n1 -4\n2 -1
Answer
Explanation:
Step1: Understand local - max/min
A local maximum is a point where the function value is greater than the values at nearby points, and a local minimum is a point where the function value is less than the values at nearby points.
Step2: Identify local maximum
Looking at the table, the function value $f(-1)=2$. The values of $f(x)$ for $x = - 2$ and $x=0$ are $-1$, which are less than $2$. So a local maximum occurs over the interval $(-2,0)$.
Step3: Identify local minimum
The function value $f(1)=-4$. The values of $f(x)$ for $x = 0$ and $x = 2$ are $-1$, which are greater than $-4$. So a local minimum occurs over the interval $(0,2)$.
Answer:
A local maximum occurs over the interval $(-2,0)$. A local minimum occurs over the interval $(0,2)$.