Difference Quotient

[supremacy32]

This problem is a part of my homework for the week and the online tool we use to turn in homework continues to indicate I do not have the problem correct. Any help would be appreciated.

Find the difference quotient and simplify your answer:
f(x)= 4x - x²

f(4 + Δx) − f(4)

Δx

Δx ≠ 0


Ok, Here we go.

Δx = h

 

[stapel]

Find the difference quotient and simplify your answer:
f(x)= 4x - x²

f(4 + Δx) − f(4)

Δx

Δx ≠ 0


Ok, Here we go.

Δx = h

Do the first two lines indicate the original exercise? Is the rest of your post your "solution" so far? If not, what is it? If so, where is the rest (after you started with "here we go")? What is the meaning or significance of the red coloring of part of what you've posted above?

...the online too...continues to indicate I do not have the problem correct.

What is the rest of your solution? (That is, what did you do after you said "here we go"?)

Please be complete. Thank you!

 

[supremacy32]

It appears much of my original post was lost. everything I had put before "here we go" was the original problem. everything after was my work. I will attempt to repost.

Original Problem:

Find the difference quotient and simplify your answer.

f(x) = 4x -x², (f(4+ Δx) - f(4)) / Δx, Δx ≠ 0


My work:

Let Δx = h

g(x) = (4(4 + h) - (4+h)² - 4(4) - (4)²) / h
g(x) = (16 + 4h - (4+h)(4+h) - 16 - 16) / h
g(x) = (16 + 4h - 16 + 4h + 4h + h2 - 32) / h
g(x) = (h² + 12h -32) / h
g(x) = h + 12 - 32/h

The final line would be my solution, but we use an online tool (webassign) to turn in homework and it indicates that that solution is not correct. I am unsure of where I am making the mistake.

 

[Deleted member 4993]

It appears much of my original post was lost. everything I had put before "here we go" was the original problem. everything after was my work. I will attempt to repost.

Original Problem:

Find the difference quotient and simplify your answer.

f(x) = 4x -x², (f(4+ Δx) - f(4)) / Δx, Δx ≠ 0


My work:

Let Δx = h

g(x) = (4(4 + h) - (4+h)² - 4(4) - (4)²) / h
g(x) = (16 + 4h - (4+h)(4+h) - 16 - 16) / h
g(x) = (16 + 4h - 16 + 4h + 4h + h2 - 32) / h
g(x) = (h² + 12h -32) / h
g(x) = h + 12 - 32/h

The final line would be my solution, but we use an online tool (webassign) to turn in homework and it indicates that that solution is not correct. I am unsure of where I am making the mistake.

f(x+h) = 4*(x+h) - (x+h)^2

= 4x + 4h - (x^2 + 2xh +h^2)

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

4x + 4h - (x^2 + 2xh +h^2) - [4x - x^2]

= 4h - 2xh - h^2

= h*[4 - 2x - h]

Now continue....