Question

Two parts of the number 84 such that the product of one part and the square of the other is maximum are

• A. 42,42
• B. 40,44
• C. 50,34
• D. 28,56

Answer 1

The correct option is A 42,42

Sum of square of two parts of a number $84$,

Let, the required number are $x$ and $84-x$

Now, according to the question,

$f\left(x\right)=x^2+{(84-x)}^2$

$f^{{}^{\prime }}\left(x\right)=2x+2(84-x)(-1)$ ……..(2)

For maxima and minima,

$f^{{}^{\prime }}\left(x\right)=0$

$2x+2(84-x)(-1)=0$

$4x=168$

$x=42$

Differentiate equation 2^nd with respect to x,

${f^{{}^{\prime }}}^{{}^{\prime }}\left(x\right)=2-2(0-1)=4$

Hence, the function $f\left(x\right)=x^2+{(84-x)}^2$is minimum.

So, required number are $42$ and $42$.

Hence, this is the answer.