2.4 関数の性質

1.

(a) $${\xi = \frac{3}{2}}$$ (b) $${\xi = \sqrt{\frac{13}{3}}}$$ (c) $${\xi = \frac{1}{\sqrt{2}}}$$

2.

(a) $(-\infty, 0)$で上に凸， $(0,\infty)$で下に凸, $x = -1$で極大値$4$，$x = 1$で極小値0, 変曲点$(0,2)$

(b) $(-\infty, 0)$で上に凸， $(0,\infty)$で下に凸, $x = -1$で極大値$-2$，$x = 1$で極小値$2$

=2.6zw =1(c) 上に凸 $(-\infty, -1)$，下に凸 $(-1, \infty)$, $${x = -1 -\frac{\sqrt{3}}{3}}$$で極大値 $${\frac{2\sqrt{3}}{9}}$$， $${x = -1 + \frac{\sqrt{3}}{3}}$$で極小値 $${-\frac{2\sqrt{3}}{9}}$$, 変曲点$(-1,0)$

=2.6zw =1(d) 上に凸 $(-\infty, -\sqrt{3}), (0, \sqrt{3})$，下に凸 $(-\sqrt{3}, 0), (\sqrt{3},\infty)$, $x = -1$で極小値 $${-\frac{1}{2}}$$，$x = 1$で極大値 $${\frac{1}{2}}$$, 変曲点 $${(-\sqrt{3}, -\frac{\sqrt{3}}{4}), (0,0), (\sqrt{3}, \frac{\sqrt{3}}{4})}$$

=2.6zw =1(e) 上に凸$(-2,1)$，下に凸 $(-\infty,-2), (1,\infty)$, $x = -2$と$x = 1$で極小値0， $x = -\frac{1}{2}$で極大値 $\frac{9}{4}$

3.

(a) $400$ (b) $${\frac{32\sqrt{3}}{9}}$$ =2.6zw =1(c) $${\frac{64\sqrt{2}}{3}}$$ (d) $${\frac{1}{2}}$$