y'=6cos2x=0
cos2x=0 2x=П/2+Пk x=П/4+Пk/2
П/4; 3П/4
y''=-12sin2x
y''(П/4)<0 максимум
y''(3П/4)>0 минимум
y(П/4)=3*sinП/2+1=4
y(3П/4)=3sin3П/2+1=-2
1) 3х-10=х+6
3х-х-10=6
3х-х=6+10
2х=6+10
2х=16
х=8
Разделить числитель и знаменатель на 2 = 1/5
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>