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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=

Sagot :

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]

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