determine the location and value of the absolute extreme values of f on the given interval, if they…

determine the location and value of the absolute extreme values of f on the given interval, if they exist.\nf(x)=x² - 5 on -3,4\nwhat is/are the absolute maximum/maxima of f on the given interval? select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.\na. the absolute maximum/maxima is/are at x=\n(use a comma to separate answers as needed.)\nb. there is no absolute maximum of f on the given interval.

determine the location and value of the absolute extreme values of f on the given interval, if they exist.\nf(x)=x² - 5 on -3,4\nwhat is/are the absolute maximum/maxima of f on the given interval? select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.\na. the absolute maximum/maxima is/are at x=\n(use a comma to separate answers as needed.)\nb. there is no absolute maximum of f on the given interval.

Answer

Explanation:

Step1: Find the derivative of the function

The function is (f(x)=x^{2}-5). The derivative (f^{\prime}(x) = 2x). Set (f^{\prime}(x)=0), so (2x = 0), which gives (x = 0).

Step2: Evaluate the function at critical points and endpoints

  • For (x=-3): (f(-3)=(-3)^{2}-5=9 - 5=4).
  • For (x = 0): (f(0)=0^{2}-5=-5).
  • For (x = 4): (f(4)=4^{2}-5=16 - 5 = 11).

Answer:

A. The absolute maximum/maxima is/are at (x = 4)