Functions Question?

Question

If the prob is find
f (x + (triangle symbol)x) - f(x) for
f(x) = 2x^2 + 3x + 1

Do I plug in the f(x) equation (2x^2 + 3x + 1) every time I see an 'x' in the equation f (x + (triangle symbol)x) - f(x)?

OR
do I just plug in the f(x) equation when I see 'f(x)' together in the equation (which is once)

Answer 1

I think you reduce 2x^2 + 3x + 1 down to it's simplest form, an then divide by X to get the function. Not 100% sure though. It's been awhile.

Answer 2

what is the change (delta, or if you prefer triangle symbol) in x. Does the problem give you an initial value and a final value?

What this is saying is, you are subtracting the initial value from the final value of f(x).

[2(x+deltax)^2 +3(x+deltax) +1 ] - [2x^2 + 3x +1 ]

Answer 3

Anytime I write h, I mean (triangle symbol)x. That will make it much easier for you to read.

f(x + h) - f(x) means to substitute (x + h) for all the x's in f(x) and then subtract the original f(x) from that result.

In this case, f(x) = 2x² + 3x + 1
So, f(x + h) = 2(x + h)² + 3(x + h) + 1
Simplify f(x + h) to 2(x² + 2xh + h²) + 3x + 3h + 1
This becomes f(x + h) = 2x² + 4xh + 2h² + 3x + 3h + 1
f(x + h) - f(x) = 2x² + 4xh + 2h² + 3x + 3h + 1 - (2x² + 3x + 1)
f(x + h) - f(x) = 2x² + 4xh + 2h² + 3x + 3h + 1 - 2x² - 3x - 1
f(x + h) - f(x) = 4xh + 2h² + 3h

Answer 4

call Dx = h
so you have to calculate
f(x+h) -f(x) = 2(x+h) ^2 +3(x+h)+1-(2x^2+3x+1)=4x*h+h^2+3h

Answer 5

To find f(x+deltax) replace x with (x+deltax) every place x appears in f(x).