Solution 2.3:7c

From Förberedande kurs i matematik 1

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m (Lösning 2.3:7c moved to Solution 2.3:7c: Robot: moved page)
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If we complete the square
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<math>x^{2}+x+1=\left( x+\frac{1}{2} \right)^{2}-\left( \frac{1}{2} \right)^{2}+1=\left( x+\frac{1}{2} \right)^{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
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<math>x+\frac{1}{2}</math>
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sufficiently large. Hence, there is no maximum value.

Revision as of 11:18, 21 September 2008

If we complete the square


\displaystyle x^{2}+x+1=\left( x+\frac{1}{2} \right)^{2}-\left( \frac{1}{2} \right)^{2}+1=\left( x+\frac{1}{2} \right)^{2}+\frac{3}{4}


we see on the right-hand side that we can make the expression arbitrarily large simply by choosing \displaystyle x+\frac{1}{2} sufficiently large. Hence, there is no maximum value.

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