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.\n$f(x)=x^{2}-5$ 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.\n$f(x)=x^{2}-5$ 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). Using the power rule ((x^{n})^\prime = nx^{n - 1}), the derivative (f^\prime(x)=2x).

Step2: Find the critical points

Set (f^\prime(x) = 0), so (2x=0), which gives (x = 0). The critical point (x = 0) lies within the interval ([-3,4]).

Step3: Evaluate the function at the critical point and endpoints

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

Answer:

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