Question

The function = 3describes the volume of a cube, , in cubic inches, whose length, width, and height each measure inches. Find the (instantaneous) rate of change of the volume with respect to when = 3 ℎ.

Answer 1

The correct structure of the question is as follows:

The function f(x) = x^3 describes a cube's volume, f(x) in cubic inches, whose length, width, and height each measures x inches. If x is changing, find the (instantaneous) rate of change of the volume with respect to x at the moment when x = 3 inches.

Answer:

Explanation:

Given that:

f(x) = x^3

Then;

V = x^3

The rate whereby V is changing with respect to time is can be determined by taking the differentiation of V

dV/dx = 3x^2

Now, at the moment when x = 3;

dV/dx = 3(3)^2

dV/dx = 3(9)

dV/dx = 27 cubic inch per inch

Suppose it is at the moment when x = 9

Then;

dV/dx = 3(9)^2

dV/dx = 3(81)

dV/dx = 243 cubic inch per inch