Question for math-enabled people
Why is it in this problem: f(x) = 4x^2 - 2x, calculate: f(x+h) - f(x) / h
That f(x+h) equals 4(x+h)^2 - 2(x+h) ? I understand that it's a substitution of (x+h) for each instance of x in f(x) = 4x^2 - 2x, but...
Oh, wait, I think I understand now. I tried putting a number in instead of (x+h) and it made sense. XD; But I already typed this, so I might as well post it. I'll probably get confused on this function substitution thing anyways. oo; I'm still not able to figure out how to write something as a function of something else. Like this one:
You're making a soft-drink can, blah blah. The ratio of the height to the radius is 4. Write the volume of the can as a function of the radius r, and the volume of the can as a function of height h.
That's just an example, so I looked at the answer, but it's not quite clicking. o_o; The first is:
V(r) = πr^2h = πr^2(4r) = 4πr^3
...what exactly are they doing there?
That f(x+h) equals 4(x+h)^2 - 2(x+h) ? I understand that it's a substitution of (x+h) for each instance of x in f(x) = 4x^2 - 2x, but...
Oh, wait, I think I understand now. I tried putting a number in instead of (x+h) and it made sense. XD; But I already typed this, so I might as well post it. I'll probably get confused on this function substitution thing anyways. oo; I'm still not able to figure out how to write something as a function of something else. Like this one:
You're making a soft-drink can, blah blah. The ratio of the height to the radius is 4. Write the volume of the can as a function of the radius r, and the volume of the can as a function of height h.
That's just an example, so I looked at the answer, but it's not quite clicking. o_o; The first is:
V(r) = πr^2h = πr^2(4r) = 4πr^3
...what exactly are they doing there?