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?

Question

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?

nowhereman · Answer

So what exactly don't you know?

anonymous · Answer

everything in the question

nowhereman · Answer

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

anonymous · Answer

x^3

nowhereman · Answer

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

anonymous · Answer

3x^2

anonymous · Answer

is this linear function

nowhereman · Answer

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.

anonymous · Answer

so is this a linear function

nowhereman · Answer

No, but you should check this yourself.