Question

The volume of a box is given by v= x3-2x2-24x.if the depth of the box be the smallest, then the depth is​

Answer 1

Answer:

Step-by-step explanation:

Where is

Answer 2

Answer:

The Depth of the box is x-6

Step-by-step explanation:

Given : The volume of a box is given by $v= x^3-2x^2-24x$

To Find: if the depth of the box be the smallest, then the depth is​?

Solution:

Volume of a box is given by $v= x^3-2x^2-24x$

Factorize the given expression :

$v= x^3-2x^2-24x$

$v= x(x^2-2x-24)$

$v= x(x^2-6x+4x-24)$

$v= x(x(x-6)+4(x-6))$

$v= x((x-6)(x+4))$

$v= x(x-6)(x+4)$

Volume of Box = $Length \times Breadth \times Depth$

Volume of given box = $v= x(x-6)(x+4)$

Since we are given that  the depth of the box be the smallest

So, The Depth of the box is x-6