I am doing difference quotient. I am to write the difference quotient in simplistic form. I am having trouble on the simplifying.
f(x) = 2x-3/4
The answer I got for this one is h-3/2h, provided h does not = 0. I wasn't sure on the simplifying at the end.
The second one is f(x) = 3(x-1)^2
The answer I got was 2hx-4x-h+2
f(x+h)-f(x) = 2(x+h)-3/4 - (2x-3/4) = 2h
So, the quotient is 2h/h = 2
Next,
f(x+h)-f(x) = 3(x+h-1)^2 - 3(x-1)^2
= 3(x^2 + 2(h-1)x + (h-1)^2) - 3(x^2-2x+1)
= 3h(2x+h-2)
Divide that by h, and you have
3(2x+h-2) = 6x+3h-6