Help for: f(x)=3x^2-3 f(x+deltax)-f(x) all over deltax

[robbob]

f(x)=3x^2-3 f(x+deltax)-f(x) all over deltax I tried to plug in the 3x^2 but i am confused what to do after

 

[tkhunny]

You are going to have to tell us exactly what the problem statement is.

When you "tried to plug in 3x^2", what did it look like? Why were you discouraged and why did you do that?

If f(x) = 3x^2 - 3, then

f(2) = 3(2)^2 - 3
f(y) = 3(y)^2 - 3
f(z+2) = 3(z+2)^2 - 3
f(Houston) = 3(Houston)^2 - 3

 

[stapel]

f(x)=3x^2-3 f(x+deltax)-f(x) all over deltax I tried to plug in the 3x^2 but i am confused what to do after

I think the above means the following:

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I was given the following function:

. . . . .$\displaystyle f(x)\, =\, 3x^2\, -\, 3$

Then I was told to plug this function into the following expression:

. . . . .$\displaystyle \dfrac{f(x\, +\, \Delta x)\, -\, f(x)}{\Delta x}$

I tried to plug just the "3x^2" into the expression, but I don't know what to do after that point.

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Assuming that the above is correct, you are likely studying the topic of "function notation" or "evaluation of functions". To learn how to evaluate a function "at" an expression (rather than at a numerical value), please try here. After you have studied at least two lessons from the list, please attempt the exercise. Start with plugging the new input (x + delta-x) in where indicated. Your start of work should look something like the following:

. . . . .$\displaystyle \dfrac{f(x\, +\, \Delta x)\, -\, f(x)}{\Delta x}$

. . . . .$\displaystyle \dfrac{\left[3(x\, +\, \Delta x)^2\, -\, 3\right]\, -\, [3x^2\, -\, 3]}{\Delta x}$

...and so forth.