Given the function, find the difference quotient

Question

f(x)=x²+2x-7

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

Answer 1

f(x)=x²+2x-7

So, f(x+h)=(x+h)²+2(x+h)-7 = x² + 2hx + h² + 2x + 2h - 7 = (x² + 2x - 7) + h² + 2h + 2hx.

Note that f(x)=x²+2x-7 so, you can write f(x+h) = f(x)+ h(h + 2 + 2x).

So, subtracting f(x) from each side gives: f(x+h)-f(x) = h(h + 2 + 2x).

Dividing by h gives (f(x+h)-f(x))/h = 2x + h + 2.

Answer 2

Hope this helps guys!!