Simultaneous equations and differentiation?

Question

Variables $u$ , $x$ and $y$ are such that $u = 2x(y-x)$ and $x + 3y = 12$ . Express $u$ in terms of $x$ and hence find the stationary value of $u$ .

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Answer 1 · 2017-08-14T15:22:00

Please see below.

Solve $x+3y=12$ for $y$

$y = 4-x/3$

Substitute in the expression for $u$

$u = 2x(4-x/3-x) = 2x(4-(4x)/3) = 8x-(8x^2)/3$

Differentiate

$(du)/dx = 8-(16x)/3$

Find $x$ values where $(du)/dx = 0$

$x = 3/2$ .

If stationary value" means the $u$ value, use $u = 8x-(8x^2)/3$ to find it.