## 2020年6月3日水曜日

### 数学 - Python - 代数学 - 1次関数、2次関数 - 2次関数の最大と最小 - 定義域と値域

1. $\begin{array}{l}2

よって値域は

$\begin{array}{l}{2}^{2}-3·2=-2

2. $\begin{array}{l}y=2\left({x}^{2}+2x\right)+5\\ =2{\left(x+1\right)}^{2}+3\\ -3

3. $\begin{array}{l}y=-\frac{1}{2}\left({x}^{2}-6x\right)+6\\ =-\frac{1}{2}{\left(x-3\right)}^{2}+\frac{9}{2}+6\\ =-\frac{1}{2}{\left(x-3\right)}^{2}+\frac{21}{2}\\ 0\le x<4\\ 6\le y\le \frac{21}{2}\end{array}$

コード

#!/usr/bin/env python3
from sympy import symbols, plot, Rational

print('16.')
x = symbols('x')
ys = [x ** 2 - 3 * x,
2 * x ** 2 + 4 * x + 5,
6 + 3 * x - x ** 2 / 2]
maxs = [4, 11, Rational(21, 2)]
mins = [-2, 3, 6]
intervals = [(x, a, b) for a, b in [(2, 4),
(-3, 1),
(0, 4)]]
for i, (y, mi, ma, interval) in enumerate(zip(ys, mins, maxs, intervals), 1):
p = plot(y, mi, ma,
interval,
ylim=(min(mins), max(maxs)),
legend=True,
show=False)
colors = ['red', 'green', 'blue', 'brown', 'orange',
'purple', 'pink', 'gray', 'skyblue', 'yellow']

for o, color in zip(p, colors):
o.line_color = color
p.save(f'sample16_{i}.png')

p.show()


% ./sample16.py
16.
/opt/local/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/sympy/plotting/plot.py:1065: MatplotlibDeprecationWarning:
The set_smart_bounds function was deprecated in Matplotlib 3.2 and will be removed two minor releases later.
self.ax[i].spines['left'].set_smart_bounds(True)
/opt/local/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/sympy/plotting/plot.py:1066: MatplotlibDeprecationWarning:
The set_smart_bounds function was deprecated in Matplotlib 3.2 and will be removed two minor releases later.
self.ax[i].spines['bottom'].set_smart_bounds(False)
%