1) y=tg 4x
y ' = <u> 4 </u>
cos² 4x
y ' (-π/4) = <u> 4 </u> = <u> 4 </u> = 4/1 = 4
cos² (-4π/4) cos²(-π)
2) y=x³ -6x²+9x-11
y ' = 3x² -12x +9
3x²-12x+9=0
x²-4x+3=0
D=16-12=4
x₁=<u>4-2 </u>= 1
2
x₂=<u>4+2 </u>= 3
2
Ответ: 1 и 3.
<span>(1/3)^х = 27</span>
<span>x=2/1:1/3</span>
<span>x=27*3=81</span>
<span>x=81</span>
2cos³x=cosx
2cos³x-cosx)=0
cosx(2cos²x-1)=0
cosx*cos2x=0
cosx=0⇒x=π/2+πn
cos2x=0⇒2x=π/2+πn⇒x=π/4+πn/2
1/cos^2a+tga/ctg(-a)=1 (по формуле приведения)
1/cos^2a-tga^2=1 (ctga=1/tga)
1/cos^2a-sin^2a/cos^2a=1 (tg^2a=sin^2a/cos^2a)
(1-sin^2a)/cos^2a=1
cos^2a/cos^2a=1
1=1