Question

Find two positive number x and y, such that x+y=60and xy3 is maximum.
$find \: two \: positive \: number \: x \: and \: y \: such \: that \: x + y \: such \: that \:x+y=60 \: and \: xy {}^{3} \: maximum.$

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Answer 1

Step-by-step explanation:

The two numbers are x and y such that x + y = 60.

⇒ y = 60 − x

Let f(x) = xy3.

∴By second derivative test, x = 15 is a point of local maxima of f. Thus, function xy3 is maximum when x = 15 and y = 60 − 15 = 45.

Hence, the required numbers are 15 and 45.