which interval for the graphed function has a local minimum of 0?\n-3,-2\n-2,0\n1,2\n2,4
which interval for the graphed function has a local minimum of 0?\n-3,-2\n-2,0\n1,2\n2,4
Answer
Explanation:
Step1: Understand local minimum
A local minimum is a point where the function has a lower - value than its neighboring points.
Step2: Check each interval
- For the interval $[-3,-2]$: The function value at $x = - 2.5$ is $0$. And in the neighborhood of $x=-2.5$ within the interval $[-3,-2]$, the function value at $x = - 2.5$ is the lowest.
- For the interval $[-2,0]$: The function value at $x = 0$ is $0$, but there are lower function values in the neighborhood within this interval (e.g., near $x=-1.56$).
- For the interval $[1,2]$: The function values in this interval are all above $0$.
- For the interval $[2,4]$: The function value at $x = 3$ is $0$, but there are lower function values in the neighborhood within this interval (e.g., near the left - hand side of the interval).
Answer:
$[-3,-2]$