Find the x - varied of all points where the function below has any relative extr

Question

Find the x - varied of all points where the function below has any relative extrema. Find the value(s) of any relative extrema. f(x) = - x2 + x - 3 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The function has a relative maximum at the point(s) (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) The function has no relative maximum. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The function has a relative minimum at the point(s) (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) The function has no relative minimum.

Explanation / Answer

f(x)= -x^2+x-3
f'(x)= -2x+1
f'(x)= 0
gives x=1/2

f''(x)=-2
so x=1/2is maxima

f(1/2)=-1/4 +1/2 -3
          = -3+1/4
          = -11/4

Ans: A The function has relative maximum at the points (1/2, -11/4)

ANS:B The function has no relative minimum

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