anonymous
  • anonymous
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?
Mathematics
schrodinger
  • schrodinger
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nowhereman
  • nowhereman
So what exactly don't you know?
anonymous
  • anonymous
everything in the question
nowhereman
  • nowhereman
If a cube has all its side length equal to a length x, what is its volume?

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anonymous
  • anonymous
x^3
nowhereman
  • nowhereman
That is what they by the volume function depending on the side length. Next calculate the gradient (=derivative) of this function.
anonymous
  • anonymous
3x^2
anonymous
  • anonymous
is this linear function
nowhereman
  • 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.
anonymous
  • anonymous
so is this a linear function
nowhereman
  • nowhereman
No, but you should check this yourself.

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