as we can know for Q_1 , set the funvction in question as f(x)
and make the first step as:
a=1,f(x)=x^2 −7x+3ln x
df(x)=2x−7+(3/x)=h(x)
set h(x)=0⇒x=(1/2)&x=3
so,the monotonicity of f(x) is f(n)<f((1/2))_(∣n<(1/2)) ,f((1/2))>f(2),f(2)<f(p)_(∣p>2.)
Q_1 has been proved finished
Q_(2 ) ,set ax^2 −(a+6)x+3ln x>−6 when x∈[2,3e],
make the f(x) dive two part as
g(x)=ax^2 −(6+a)x&k(x)=−3(ln x+2),
the middle value of g(x) is x=((a+6)/(2a))
when x=3e, k_(min) (3e)=−15, x=2, k_(max) (2)=−3(ln 2+2)
g(2)=2a−12>k_(max) (x)⇒a>3−(3/2)ln 2
when x=(1/2)+(3/a), g(x)=−(((a+6)^2 )/(4a))>−3(ln (((a+6)/(2a)))+2)&a>0&2<(1/2)+(3/a)<3e
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