help with maximum or minimm value (1 Viewer)

[wolf7]

first question

the parabola y = 3x^2 - kx +2 is symmetrical about the line x= 1/2. find the value of k and the minimum value of the expression

second question

find the two numbers whose sum is 12 and which have a maximum product. let two numbers be x and 12-x

if you have spare time, u reakon u can answer it for me

 

[wolf7]

can ya also show working out

 

[Trev]

Q1)
You use x=-b/2a to find the line it is symmetrical about.
x=-b/2a = k/6 which you are told equals 1/2; so k/6=1/2; k=3.
Min value where x=1/2.
y=3x²-3x+2
y=3(1/2)²-3(1/2)+2 = whatever.

 

[Trev]

x, 12-x.
P (product) = x(12-x)
P=12x-x²
To find stat. point (max. point) find derivative of P.
P'=12-2x; When P'=0 x=6.
Since it is the only stationary point and it is a concave down parabola (so a max point occurs) then x=6 is a max point and two numbers are 6 and 6.

 

[wolf7]

thanx, i understand it better