<span>у=(х-3)2 e(x+1) на [-2; 4] </span><span>Найдем производную по ф-ле: (uv)' =u'v + uv'</span><span>y' = 2(x-3)ex+1 + (x-3)2 ex+1 =0 </span><span><span>ex+1 (x-3)(2+x-3) = 0</span>, ex+1 >0</span><span>x-3=0 <span>x1 = 3</span> - критическая точка</span><span>2+x-3=0, <span>x2 = 1</span> - критическая точка</span><span>Вычислим значения ф-ции на концах [-2;4] и в критических точках х1 и х2.</span><span><span>y(-2) = (-5)2e-1 =25/e</span> (≈ 25/2,7 = 9,26)</span><span><span>y(1) = (-2)2 e</span>2<span> =4е2</span><span> </span>(≈4·7.29 = 29,16)</span><span>y(3) = 0 - наименьшее значение
</span><span>y(4) = 12 ·e5 <span>= е5 - наибольшее значение </span> (≈ 143,49)</span>
<span>Представьте трёхчлен в виде квадрата двучлена:
![a) 4+4a+a^2 = (2+a)^2; \\ b) a^2-8ab+16b^2=(a-4b)^2 \\ v) 12x+x^2+36=(x+6)^2 \\ g) 16x^2-24xy+9y^2=(4x-3y)^2](https://tex.z-dn.net/?f=a%29%204%2B4a%2Ba%5E2%20%3D%20%282%2Ba%29%5E2%3B%20%5C%5C%20b%29%20a%5E2-8ab%2B16b%5E2%3D%28a-4b%29%5E2%20%5C%5C%0A%20v%29%2012x%2Bx%5E2%2B36%3D%28x%2B6%29%5E2%20%5C%5C%20g%29%2016x%5E2-24xy%2B9y%5E2%3D%284x-3y%29%5E2)
<span>Упростите выражения: </span>
![a) (2x-5)^{2}+20x = 4x^2-20x+25+20x =4x^2+25 \\ b)36c-3(1+6c)^{2}=36c-3-36c- 108c^2=-3-108c^2 \\ v)(6a+2b)^{2}-24ab=36a^2+24ab+4b^2-24ab =36a^2+4b^2 \\ g)-6x^{3}-3(x^{3}-1)^{2}=-6x^3-3x^6+6x^3-3= -3x^6-3](https://tex.z-dn.net/?f=a%29%20%282x-5%29%5E%7B2%7D%2B20x%20%3D%204x%5E2-20x%2B25%2B20x%0A%3D4x%5E2%2B25%20%5C%5C%20%0Ab%2936c-3%281%2B6c%29%5E%7B2%7D%3D36c-3-36c-%0A108c%5E2%3D-3-108c%5E2%20%5C%5C%20%0Av%29%286a%2B2b%29%5E%7B2%7D-24ab%3D36a%5E2%2B24ab%2B4b%5E2-24ab%0A%3D36a%5E2%2B4b%5E2%20%5C%5C%20%0Ag%29-6x%5E%7B3%7D-3%28x%5E%7B3%7D-1%29%5E%7B2%7D%3D-6x%5E3-3x%5E6%2B6x%5E3-3%3D%0A-3x%5E6-3)
</span>
<span>16 букетов.</span>
50:3=16.666 ( округляем до 16 ).