SOLUTION: Will someone please look this over to make sure I have it solved correctly? Using the difference quotient f(x+h)-f(x)/h: g(x) = 4x^2-5 4(x+h)^2-5-(4x^2-5)/h 4(x+h)(x+h)-5

Question 271970: Will someone please look this over to make sure I have it solved correctly?
Using the difference quotient f(x+h)-f(x)/h:
g(x) = 4x^2-5
4(x+h)^2-5-(4x^2-5)/h
4(x+h)(x+h)-5-4x^2+5/h
4(x^2+hx+hx+h^2)-5-4x^2+5/h
4x^2+8hx+4h^2-5-4x^2+5/h
4h^2+8hx/h
Answer 4h+8x

Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
Using the difference quotient f(x+h)-f(x)/h:
g(x) = 4x^2-5
1. 4(x+h)^2-5-(4x^2-5)/h
2. 4(x+h)(x+h)-5-4x^2+5/h
3. 4(x^2+hx+hx+h^2)-5-4x^2+5/h
4. 4x^2+8hx+4h^2-5-4x^2+5/h
5. 4h^2+8hx/h
Answer 4h+8x
In step 3 you have:
4(x^2+hx+hx+h^2)-5 - (4x^2-5)/h
4x^2 + 8hx + 4h^2 - 5 - 4x^2/h + 5/h
I wonder if the problem shouldn't really be:
[g(x+h) - g(x)]/h ?
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