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help with maximum or minimm value (1 Viewer)

wolf7

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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
 

Trev

stix
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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=3x<sup>2</sup>-3x+2
y=3(1/2)<sup>2</sup>-3(1/2)+2 = whatever.
 

Trev

stix
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x, 12-x.
P (product) = x(12-x)
P=12x-x<sup>2</sup>
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.
 

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