Solution 2.3:7a
From Förberedande kurs i matematik 1
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- | In the polynomial | + | In the polynomial <math>1-x^{2}</math>, only the second term depends on ''x'' and, on account of the minus sign in front of that term, the whole expression is largest when the square ''x''² is least. The quadratic term ''x''² is least when <math>x=0</math>. The polynomial's largest value is equal to <math>1-0^{2}=1\,</math>. |
- | <math>1-x^{2}</math>, only the second term depends on | + | |
- | + | ||
- | and, on account of the minus sign in front of that term, the whole expression is largest when the square | + | |
- | + | ||
- | is least. The quadratic term | + | |
- | + | ||
- | is least when | + | |
- | <math>x=0</math>. The polynomial's largest value is equal to | + | |
- | <math>1-0^{2}=1</math>. | + |
Current revision
In the polynomial \displaystyle 1-x^{2}, only the second term depends on x and, on account of the minus sign in front of that term, the whole expression is largest when the square x² is least. The quadratic term x² is least when \displaystyle x=0. The polynomial's largest value is equal to \displaystyle 1-0^{2}=1\,.