1) <u> y-8 </u> - <u>3-4y </u>= <u>y(y-8) - 2(3-4y) </u>=<u> y²-8y-6+8y </u>= <u> y²-6</u>
2y y² 2y² 2y² 2y²
2) <u> 7 </u> - <u> 56 </u> = <u> 7 </u> - <u> 56 </u> = <u>7(a+8)-56 </u>= <u> 7a+56-56 </u>=<u> 7a </u>= <u> 7 </u>
a a²+8a a a(a+8) a(a+8) a(a+8) a(a+8) a+8
3) <u> b </u> - <u> b² </u>= <u> b </u> - <u> b² </u> = <u> b(b-1)-b² </u>=<u> b²-b-b² </u>=
b+1 b²-1 b+1 (b+1)(b-1) (b+1)(b-1) b² -1
= <u> -b </u>= <u> b </u>
b² -1 1-b²
4) 3x - <u> 15x² </u>= <u> 3x(5x+2) - 15x² </u>= <u>15x² +6x -15x² </u> = <u> 6x </u>
5x+2 5x+2 5x+2 5x+2
Касательные параллельны оси абсцисс в точках экстремумов.
1) y' = 12x^3 - 84x^2 - 12x + 84 = 12(x-7)(x^2 - 1) = 12(x-7)(x-1)(x+1) = 0
x1 = -1; y(-1) = 3 + 28 - 6 - 84 + 1 = -58
x2 = 1; y(1) = 3 - 28 - 6 + 84 + 1 = 54
x3 = 7; y(7) = 3*2401 - 28*343 - 6*49 + 84*7 + 1 = -2106
2) y' = -2sin 2x + 5sin x = -4sin x*cos x + 5sin x = sin x*(5 - 4cos x) = 0
sin x = 0; x1 = 2pi*k; y(x1) = cos(4pi*k) - 5cos(2pi*k) = 1 - 5*1 = -4
x2 = pi + 2pi*k; y(x2) = cos(2pi+4pi*k) - 5(pi+2pi*k) = 1 - 5(-1) = 6
5 - 4cos x = 0; cos x = 5/4 > 1 - решений нет.
3) y' = (x - 4)^3 + x*3(x - 4)^2 = (x - 4)^2*(x - 4 + 3x) = (x - 4)^2*(4x - 4) = 0
x1 = x2 = 4; y(4) = 0
x3 = 1; y(1) = 1*(1 - 4)^3 = 1(-3)^3 = -27
<span>√(7* (19/32))=√(133/32)=√133/√32=√(133)/2.
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