Question

If/the sum of 2 numbers is 3 then the maximum value/of the product of first and square of 2nd is

Answer 1

Answer:

$\frac{32}{27}$

Step-by-step explanation:

Let numbers x and 2-x

we have to find

$\: max \: \: \: {x}^{2} (2 - x)$

Assuming x and 2-x are positive otherwise maximum value will be infinite

It's derivative = 0

$4x - 3 {x}^{2} = 0 \\\implies \: x =0 \: and \: \frac{4}{3}$

So critical values are 0 and 16/9×2/3=32/27 Confirm second derivative test to check if it is maxima or minima