y=20-4x. the volume of the box is V cm ^3 find in terms of x
![y204x the volume of the box is V cm 3 find in terms of x class=](https://us-static.z-dn.net/files/d53/a71548936619e3b036e1615deca92818.png)
b. The volume of a box is computed as follows:
[tex]V=\text{length}\cdot\text{width}\cdot\text{height}[/tex]Substituting with length = 3x, width = x, and heigth = y = 20 - 4x, we get:
[tex]\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}[/tex]c.
[tex]\frac{d}{dx}(x^n)=n\cdot x^{n-1}[/tex]Applying this rule to V, we get:
[tex]\begin{gathered} \frac{dV}{dx}=60\cdot2\cdot x-12\cdot3\cdot x^2 \\ \frac{dV}{dx}=120x-36x^2 \end{gathered}[/tex]