We wish to minimize this function so we recall the first

Last updated: 7/15/2023

We wish to minimize this function so we recall the first derivative test for absolute extrema values which states that if c is a critical number of a continuous function f defined on an interv then the following holds If f x 0 for all x c and f x 0 for all x c then f c is the absolute maximum value of f If f x 0 for all x c and f x 0 for all x c then f c is the absolute minimum value of f To apply this test we must first find f x Doing so gives the following result f x x 56x f x Setting this derivative equal to 0 and solving for x gives the following result X Applying the test we see that there is an absolute Select at this value of x