1 Answer
Solution :-
Suppose the given two numbers be x and y. Now, x + y = 15 ….. (1)
Then we have, z = x2 y3 z = x2 (15 – x)3 (from the equation 1)
\( \dfrac{dz}{dx}\) = 2x(15 - x)3 - 3x2(15 - x)2
For the maximum or minimum values of z, we must have
\( \dfrac{dz}{dx}\) = 0
Hence, z is the maximum when x = 6 and y = 9
Therefore, the required two parts into which 15 should be divided are 6 and 9.
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