Выражаем y из первого уравнения:
y=2,5x-15
Подставляем во второе:
75x^2+24(2,5x-15)^2=1800
75x^2+24(6,25x^2-75x+225)=1800
75x^2+150x^2-1800x+5400-1800=0
225x^2-1800x+3600=0
3x^2-24x+48=0
x^2-8x+16=0
(x-4)^2=0
x=4
5*4-2y-30=0
20-30=2y
-10=2y
y= -5
Ответ: в точке (4;-5)
Координаты точки пересечения графиков функции у=√х и у=2-х.
Решение. Способ 1<span><span>f′</span>(x)=<span><span>(<span><span>4⋅x−7 / </span><span>x2</span></span>)</span>′</span>=
</span><span>=(<span><span><span><span>(4⋅x−7)</span>′</span>⋅<span>x2</span>−<span>(4⋅x−7)</span>⋅<span><span>(<span>x2</span>))</span>′ / </span></span><span><span>(<span>x2</span>)</span>2</span></span>=
</span><span>=<span><span><span><span>(4⋅x)</span>′</span>⋅<span>x2</span>−<span>(4⋅x−7)</span>⋅2⋅x</span><span><span>(<span>x2</span>)</span>2</span></span>=
</span><span>=<span><span>4⋅<span>x2</span>−<span>(4⋅x−7)</span>⋅2⋅x / </span><span><span>(<span>x2</span>)</span>2
</span></span></span>Ответ:<span>f′</span>(x)=<span><span>4⋅<span>x2</span>−<span>(4⋅x−7)</span>⋅2⋅x / </span><span><span>(<span>x2</span>)</span><span>2</span></span></span>
![f(x) = \sqrt[4]{x}](https://tex.z-dn.net/?f=f%28x%29+%3D+%5Csqrt%5B4%5D%7Bx%7D+)
