JAMB 2000 · UME · Q20

A trader realizes $10x - x^2$ naira profit from the sale of $x$ bags of corn. How many bags will give him the maximum profit?

Worked solution (try it first)

The profit is greatest where its gradient is zero: $\frac{d}{dx}(10x - x^2) = 10 - 2x$ .
$10 - 2x = 0$ , so $x = 5$ .
The second derivative is $-2 < 0$ , so this is a maximum: 5 bags, option B.