Find the difference quotient of f, that is, find
f(x+h) - f(x)
---------
h

for these functions:
f(x) = -4x+1

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

Question

Find the difference quotient of f, that is, find 
f(x+h) - f(x)
---------
        h

for these functions:
f(x) = -4x+1

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

bahrom7893 · Answer

1) -4
2) 2x-1

anonymous · Answer

I originally put 2x-1 & it was not the right answer

bahrom7893 · Answer

is it the limit as h->0?

anonymous · Answer

h does not equal 0

anonymous · Answer

yeah, 2x-1 is the derivative, but its not asking for the lim as h-->0

bahrom7893 · Answer

ohh I see wait up..for the 2nd one
Here:
(x+h)^2-(x+h)+4 - (x^2 -x +4)
---------------------------
                   h

anonymous · Answer

$$f(x+h) = (x+h)^{2}-(x+h)+4$$
$$= x^{2}+2xh+h^{2}-x-h+4$$
$$\frac{f(x+h)-f(x)}{h} = \frac{x^{2}+2xh+h^{2}-x-h+4-x^{2}+x-4}{h} = \frac{2xh+h^{2}-h}{h}$$

bahrom7893 · Answer

Simplify:
[x^2+2xh+h^2-x-h+4-x^2-x+4]/h

anonymous · Answer

Dividing out the h we get:
$$2x+h-1$$
which would be you answer

anonymous · Answer

notice if you took the lim as h went to 0 you would get the derivative, which is 2x-1

anonymous · Answer

thanks!