Help - maths problem?

Question

f(x)=2x²+4x+5 where x is Real.

By considering the identity 2x²+4x+5 ≡ 2(x+A)²+B,where A and B are constants,

find the greatest value of 1/f(x)

................obviously i found that A is 1 and B is 3...but that's not the ans...Please help by giving me the working also pls .thankx

Answer 1

Then 1/f(x) = 1/(2x^2 +4x +5 ),then it has max & min when the derivitive

is zero,

              f ' (x)=   0- (4x+4)/(2x^2 +4x + 5) ^ 2=0

then 4x+4=0,at x=- 1 it is eighter min or max.

Answer 2

1/f(x) will be a max when f(x) is a minimum

ie at x = -A