F(x)=4√x-1/(10x) f`(1/9)-?
f`(x)=4*(1/(2*√x)(1/10)/x²
f`(1/9)=4*(1/(2*√(1/9))-(1/10)/(1/9)²=4*(1/(2*1/3)-(1/10)/(1/81)=
=4*(3/2)-81/10=12/2-8,1=6-8,1=-2,1
f(x)=(1-x)² f(x)=f`(x)
f`(x)=2*(1-x)*(-1)=2x-2 ⇒
2x-2=(1-x)²
2x-2=1-2x+x²
x²-4x+3=0 D=4
x₁=3 x₂=1.
f`(x)=((x²+5)/(x-2))`=(2x*(x-2)-(x²+5)*1)/(x-2)²=(2x²-4x-x²-5)/(x-2)²=
=(x²-4x-5)/(x-2)²
x²-4x-5=0 D=36
x₁=5 x₂=-1 ⇒
(x-5)(x+1)/(x-2)²
(x-2)²≥0 x-2≠0 x≠2
-∞_____+_____-1_____-_____2_____-______5_____+_____+∞
Ответ: x∈(-1;2)U(2;5).