Find the maximum or minimum value of the function. f(x) = x2 + x + 1

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Find the maximum or minimum value of the function.

f(x) = x2 + x + 1

Jul 8th, 2015

Hello!

Make a perfect square:
f(x) = x^2 + x + 1 = (x + 1/2)^2 - 1/4 + 1 = (x + 1/2)^2 +3/4.

(x + 1/2)^2 >= 0, and =0 only for x=-1/2.

So f has a minimum at x=-1/2 and the minimum value is f(-1/2) = 3/4.

Answer: minimum value is 3/4  (reached at x=-1/2).

Please ask if anything is unclear.
Jul 8th, 2015

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Jul 8th, 2015
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Jul 8th, 2015
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