Question

divide 80 into two parts such that their product is maximum​

Answer 1

Answer:

if we divide 80 into two parts then the product will be 40

Answer 2

When $80$ is divided into two parts, then maximum value of their product is $1600$.

Step-by-step explanation:

Let, the two parts of $80$ be $x$ and $(80 - x)$.

Then their product is $x(80-x)=80x-x^{2}$

We have to find $\bold{Max\{80x-x^{2}\}}$

Here, $f(x)=(-1)x^{2}+80x+0$

Then $-\dfrac{b}{2a}=-\dfrac{80}{-2}=40$

Thus, maximum of $f(x)$

$=80(40)-(40)^{2}$

$=3200-1600$

$=\bold{1600}$

NOTE: We must know that the maximum value of a quadratic expression of the form $f(x)=ax^{2}+bx+c$ is given by $f(-\dfrac{b}{2a})$