Solution 2.3:7c
From Förberedande kurs i matematik 1
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- | {{ | + | If we complete the square, |
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- | {{ | + | {{Displayed math||<math>x^{2}+x+1=\Bigl(x+\frac{1}{2}\Bigr)^{2}-\Bigl(\frac{1}{2} \Bigr)^{2}+1 = \Bigl(x+\frac{1}{2}\Bigr)^{2} + \frac{3}{4}\,,</math>}} |
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+ | we see on the right-hand side that we can make the expression arbitrarily large simply by choosing <math>x+\tfrac{1}{2}</math> sufficiently large. Hence, there is no maximum value. |
Current revision
If we complete the square,
\displaystyle x^{2}+x+1=\Bigl(x+\frac{1}{2}\Bigr)^{2}-\Bigl(\frac{1}{2} \Bigr)^{2}+1 = \Bigl(x+\frac{1}{2}\Bigr)^{2} + \frac{3}{4}\,, |
we see on the right-hand side that we can make the expression arbitrarily large simply by choosing \displaystyle x+\tfrac{1}{2} sufficiently large. Hence, there is no maximum value.