Answers

The Brainliest Answer!
2015-07-22T12:30:42+05:30

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Let the two parts be x and y.
x+y = 84
⇒ y = (84-x)

You need to maximise the product of "one part" and "the square of other"
Let one part = (84-x)
square of other part = (x)² = x²
product, p = x² × (84-x) = 84x² - x³

 \frac{dp}{dx}=0\\ \\ \Rightarrow  \frac{d}{dx}(84 x^{2} -x^3)=0  \\ \\ \Rightarrow 84 \times 2x - 3 x^{2} =0\\ \\ \Rightarrow 168x-3x^2=0\\ \\ \Rightarrow 3x(56-x)=0\\ \\ \Rightarrow x=0\ or\ 56 \\\\

For maximum, \frac{d^2p}{dx^2} \ \textless \  0

\frac{d^2p}{dx^2}= \frac{d^2(84 x^{2} -x^3)}{dx^2}= \frac{d}{dx}(168x-3x^2)=168-6x   \\ \\at\ x=0\\ 168-6x=168-6 \times 0=168\ \textgreater \ 0\ \ \ (condition\ not\ satisfied) \\ \\at\ x=56\\ 168-6x=168-6 \times 56=-168\ \textless \ 0\ \ \ (condition\ satisfied)

So x = 56,
y = 84 - x = 84- 56 = 28

So the two parts are (28,56)
2 5 2