by inspecting the graph of the function, find the absolute maximum and absolute minimum on the given…

by inspecting the graph of the function, find the absolute maximum and absolute minimum on the given interval.\ng(x)=x² - 2 on -5,4\nfind the absolute minimum. select the correct choice below and, if necessary, fill in the answer boxes to complete your choice\nthe absolute minimum is -2 at x = 0\n(use a comma to separate answers as needed )\nthere is no absolute minimum\nfind the absolute maximum. select the correct choice below and, if necessary, fill in the answer boxes to complete your choice\nthe absolute maximum is at x =\n(use a comma to separate answers as needed )\nthere is no absolute maximum

by inspecting the graph of the function, find the absolute maximum and absolute minimum on the given interval.\ng(x)=x² - 2 on -5,4\nfind the absolute minimum. select the correct choice below and, if necessary, fill in the answer boxes to complete your choice\nthe absolute minimum is -2 at x = 0\n(use a comma to separate answers as needed )\nthere is no absolute minimum\nfind the absolute maximum. select the correct choice below and, if necessary, fill in the answer boxes to complete your choice\nthe absolute maximum is at x =\n(use a comma to separate answers as needed )\nthere is no absolute maximum

Answer

Explanation:

Step1: Analyze the function (g(x)=x^{2}-2)

This is a parabola opening upwards ((a = 1>0) in (y = ax^{2}+bx + c)) with vertex at ((0,-2)).

Step2: Evaluate the function at the endpoints of the interval ([-5,4])

  • When (x=-5), (g(-5)=(-5)^{2}-2=25 - 2=23).
  • When (x = 4), (g(4)=4^{2}-2=16-2 = 14).

Answer:

The absolute maximum is (23) at (x=-5).