## anonymous 5 years ago the relatioship between the volume of a cube and the lenght of its side is a function. the volume is a fuction of the side lenght. 1)is this a linear function? justify. 2)describe the way in which the gradient of this function changes? 3)what is the average gradient of the function if the length is 2?

1. nowhereman

So what exactly don't you know?

2. anonymous

everything in the question

3. nowhereman

If a cube has all its side length equal to a length x, what is its volume?

4. anonymous

x^3

5. nowhereman

That is what they by the volume function depending on the side length. Next calculate the gradient (=derivative) of this function.

6. anonymous

3x^2

7. anonymous

is this linear function

8. nowhereman

A linear function f(x) must satisfy the conditions $f(x+y) = f(x)+f(y)\quad f(αx) = αf(x)$ for any real numbers x,y,α.

9. anonymous

so is this a linear function

10. nowhereman

No, but you should check this yourself.