which interval contains a local minimum for the graphed function?\n-4, -2.5\n-2, -1\n1, 2\n2.5, 4\n(-2.5…

which interval contains a local minimum for the graphed function?\n-4, -2.5\n-2, -1\n1, 2\n2.5, 4\n(-2.5, 0)\n(1.7, 0.7)\n(3.44, 0)\n(-0.44, -4.3)\n(3, -4)

which interval contains a local minimum for the graphed function?\n-4, -2.5\n-2, -1\n1, 2\n2.5, 4\n(-2.5, 0)\n(1.7, 0.7)\n(3.44, 0)\n(-0.44, -4.3)\n(3, -4)

Answer

Answer:

D. $[2.5,4]$

Explanation:

Step1: Recall local - minimum definition

A local minimum is a point where the function changes from decreasing to increasing.

Step2: Analyze intervals

  • In the interval $[-4,-2.5]$, the function is decreasing.
  • In the interval $[-2,-1]$, the function is increasing.
  • In the interval $[1,2]$, the function is increasing.
  • In the interval $[2.5,4]$, the function has a local - minimum near $x = 3$ where the function value is $y=-4$. The function is decreasing before $x = 3$ and increasing after $x = 3$ in this interval.