Гафiк перетина"э" вiсь ординат у точцi (0;y). Пiдставимо пiд х нуль, тодi y набува"э" значення у(0)=18*0^2+3*0-2=-2
Вiдповiдь: - 2.
<span>y - скорость теплохода </span>
<span>a - скорость течения </span>
<span>120/(y-a)=5 </span>
<span>180/(y+a)=6 </span>
<span>5y-5a=120 </span>
<span>6y+6a=180 </span>
<span>y-a=24 </span>
<span>y+a=30 </span>
<span>просуммируем 2 уравнения, получим: </span>
<span>2x=54 </span>
<span>x=27 -> y=3</span>
=)
1)-10x^2 +3x+1=0
d=b^2 - 4ac = 3^2 - 4*(-10)*1 = 9+40 = 49
VD = V49 = 9
-b+ - VD
Xo = ----------------
2a
x1 = -3+9/2 *(-10) = 6/-20 = -3/10
x2 = -3-9/2*(-10) = -12/-20 = 3/5
OTBET: x=-3/10 i x=3/5
2) -3x^2 - 2<em>x</em> +8=0
D = b^2 - 4ac = -2^2 -4*(-3)*8= 4+96 = 100
VD = V100 = 10
x1 = 2+10/2*(-3) = 12/-6 = -2
x2 = 2-10/2*(-3) = -8/-6 = 4/3
3) 3x^2+6+11x=0
3x^2+11x+6=0
D = 11^2 - 4*3*6 = 121 - 72 = 49
VD = V49 = 7
x1 = -6+7/2*3 = 1/6
x2 = -6-7/2*3 = -13/6 = -2 1/6
4) 15+17x-4x^2=0
-4x^2+17x+15 = 0
D = 17^2 - 4*(-4)*15 = 289 +240 = 529
VD = V529 = 23
x1 = -17+23/2*(-4) = 6/-8 = -3/4
x2 = -17-23/2*(-4) = -40/-8 = 5
помогла?
поблагодарите!
![y=3x^4+8x^3-18x^2+1 \\ \\ y'=12x^3+24x^2-36x=12x(x^2+2x-3) \\ \\ y'=0 \\ 12x(x^2+2x-3)=0 \\ x_1=0 \\ x^2+2x-3=0 \\ D=4+12=16 \\ x= \frac{-2+-4}{2} = \left \{ {{x_2=-3} \atop {x_3=1}} \right. \\ \\ y'=12x(x+3)(x-1)](https://tex.z-dn.net/?f=y%3D3x%5E4%2B8x%5E3-18x%5E2%2B1+%5C%5C++%5C%5C+y%27%3D12x%5E3%2B24x%5E2-36x%3D12x%28x%5E2%2B2x-3%29+%5C%5C++%5C%5C+y%27%3D0+%5C%5C+12x%28x%5E2%2B2x-3%29%3D0+%5C%5C+x_1%3D0+%5C%5C+x%5E2%2B2x-3%3D0+%5C%5C+D%3D4%2B12%3D16+%5C%5C+x%3D+%5Cfrac%7B-2%2B-4%7D%7B2%7D+%3D+%5Cleft+%5C%7B+%7B%7Bx_2%3D-3%7D+%5Catop+%7Bx_3%3D1%7D%7D+%5Cright.++%5C%5C++%5C%5C+y%27%3D12x%28x%2B3%29%28x-1%29)
- + - +
-----------------|-----------------|-----------------|---------------->x
-3 0 1
min max min
![y(-3)=3(-3)^4+8(-3)^3-18(-3)^2+1=243-216-162+1=-134 \\ \\ y(0)=3*0+8*0-18*0+1=1 \\ \\ y(1)=3*1+8*1-18*1+1=-6](https://tex.z-dn.net/?f=y%28-3%29%3D3%28-3%29%5E4%2B8%28-3%29%5E3-18%28-3%29%5E2%2B1%3D243-216-162%2B1%3D-134+%5C%5C++%5C%5C+y%280%29%3D3%2A0%2B8%2A0-18%2A0%2B1%3D1+%5C%5C++%5C%5C+y%281%29%3D3%2A1%2B8%2A1-18%2A1%2B1%3D-6)
функция убывает на промежутке x∈
![(-\infty; -3)U(0;1)](https://tex.z-dn.net/?f=%28-%5Cinfty%3B+-3%29U%280%3B1%29)
функция возрастает на промежутке x∈
![(-3;0)U(1;+\infty)](https://tex.z-dn.net/?f=%28-3%3B0%29U%281%3B%2B%5Cinfty%29)
точка максимума (0;1)
точки минимума (-3;-134) и (1;-6)