Find the max value of f(x)=-5x²+6x-5?

Find the max value of f(x)=－5x^2+6x－5?
Sol
－5x^2+6x－5
=(－5x^2+6x)－5
=－5(x^2－1.2x)－5
=－5(x^2－1.2x+0.36)+5*0.36－5
=－5(x－0.6)^2－3.2
(x－0.6)^2>=0
－(x－0.6)^2<=0
－5(x-0.6)^2－3.2<=－3.2
f(x)<=－3.2
or
f(x)=－5x^2+6x－5
f’(x)=－10x+6
set f’(x)=0
－10x+6=0
x=3/5
f”(x)=－10
f”(3/5)=－10<0
max=f(3/5)
=－5*(3/5)^2+6*(3/5)－5
=－5*0.36+3.6－5
=－3.2