Question

Y=20-4x. the volume of the box is V cm ^3 find in terms of x

Answer 1

b. The volume of a box is computed as follows:

`V=\text{length}\cdot\text{width}\cdot\text{height}`

Substituting with length = 3x, width = x, and heigth = y = 20 - 4x, we get:

`\begin{gathered} V=3x\cdot x\cdot(20-4x) \\ V=3x^2(20-4x) \\ V=3x^2\cdot20-3x^2\cdot4x \\ V=60x^2-12x^3 \end{gathered}`

c.

`(d)/(dx)(x^n)=n\cdot x^(n-1)`

Applying this rule to V, we get:

`\begin{gathered} (dV)/(dx)=60\cdot2\cdot x-12\cdot3\cdot x^2 \\ (dV)/(dx)=120x-36x^2 \end{gathered}`