Y=f(a)+<span>f′</span>(a)⋅(x−a<span>)
Вычисление производной :
</span><span><span>f′</span>(x)=<span><span>(<span>−<span>x^2</span>+6⋅x+8</span>)</span>′</span>=</span><span>=<span><span>(<span>−<span>x^2</span>+6⋅x</span>)</span>′</span>=</span><span>=<span><span>(<span>−<span>x^2</span></span>)</span>′</span>+<span><span>(<span>6⋅x</span>)</span>′</span>=</span><span>=−<span><span>(<span>x^2</span>)</span>′</span>+6=</span><span>=−2⋅x+6
</span>Подставим числа <span>a=−2;f(a)=−8;<span>f′</span>(a)=10</span><span> в формулу</span>
<span>y=−8+10⋅(x+2)=10x+12
ответ : y=10x+12</span>
x^4+6x^3+9x^2-14x^2-42x+40=0
1) 8-7х=0
-7х=-8
х= -8/-7
х=1.14
2) 0.2х-1=3-0.8х
х=4
3) (8х+5)-(3х+10)=25
8х+5-3х-10=25
5х=30
х=6
Ответ:
х²+8х+16-9а² = (х+4)²-9а² = (х+4+3а)(х+4-3а)