Divide 15 into two parts such that the square of one multiplied with the cube of the other is minimum.

Asked by Aaryan | 1 year ago |  162

##### 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.

Answered by Aaryan | 1 year ago

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