(1 point) Find the critical numbers and the intervals on which the function/(x)
ID: 2885993 • Letter: #
Question
(1 point) Find the critical numbers and the intervals on which the function/(x) = 1x + 5x-1-7, (x > 0) is increasing or decreasing the First Derivative Test to determine whether the critical number is a local minimum or maximum (or neither). . Use (Use symbolic notation and fracti no critical points.) ions where needed. Give your answer in the form of comma separated list. Enter NULL if there are The critical numbers with local minimum help (fractions) The critical numbers with local maximum: (Use symbolic notation and fractions where needed. Give your answers as intervals in the form (,"). Use inf for infinity, U for combining intervals, and appropriate type of parenthesis, or "l" depending on whether the interval is open or closed) The function increasing on help (intervals) help (intervals) The function decreasing on Note: You can earn partial credit on this problem. MARExplanation / Answer
f(x) = x+5/x-7
Find derivative as
f'(x) = 1 -5/x²
To find critical point, set f'(x) =0 and solve for x
1 -5/x² =0
x² -5 =0
x² =5
x= 5 as given x>0
hence
Local minimum critical number is 5
Local maixmum critical number is NULL
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Increasing on (5 , )
Decreasing on (0, 5)
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