Question

Difference quotient for f(x) = 4x

Answer 1

f(x + h) - f(x)
------------ = ?
h

Answer 2

I have the formula in front of me I just don't know how to apply it

Answer 3

In f(x) = 4x, the function f takes x and multiplies it by 4.

In f(x+h), the function f will take (x + h) and replace x by that to get

f(x + h) = 4*(x + h)

Agree?

Answer 4

I think so. What's confusing me is the h.

Answer 5

f(x + h) - f(x) 4x + 4h - 4x 4h
------------ = -------------- = ---- = 4
h h h

Answer 6

Don't think too much about the h.

Just ask yourself, what is f doing to what is within the ( ) of f(x).

In this case f is taking x and multiplying it by 4.

So, when (x + h) gets with f as in f(x+h), the the (x+h) is multiplied by 4.

Answer 7

Oh okay. I think I get it better now. Thank you for your help!

Answer 8

When you get on down the line in this class, the h will take on more significance.

But if f(x) = 4*x, f(x+h) will be 4*(x+h).

Just think of x in f(x) as a placeholder of sorts.

Answer 9

Yea that makes sense

Answer 10

The first time I studied this, I was confused.

Answer 11

Yeah, I think it just takes some practice to get it down completely

Answer 12

But thank you for explaining it!

Answer 13

You are welcome.