Given f(x)=3x^2-x+10, g(x)=2x-3 algebraically find & simplify the following: difference quotient f(x+h)-f(x)/h

Question

Can some one please explain the steps to me.

Answer 1

For this, you need to substitute (x + h) for x and basically plug and chug:

f(x + h) = 3(x + h)^2 - (x + h) + 10
= 3(x^2 + 2hx + h^2) - x - h + 10
= 3x^2 + 6hx + 3h^2 - x - h + 10

f(x) = 3x^2 - x + 10

f(x + h) - f(x) = (3x^2 + 6hx + 3h^2 - x - h + 10) - (3x^2 - x + 10)
= 3x^2 + 6hx + 3h^2 - x - h + 10 - 3x^2 + x - 10
= 6hx + 3h^2 - h

[f(x + h) - f(x)] / h = (6hx + 3h^2 - h)/h
= 6x + 3h - 1

g(x) has no bearing in this problem, but if you have to do the same for g(x) as we did for f(x), just follow the steps above and you'll be fine.