Given f(x)=3x^2-7x+2, determine f(x+h)-f(x)?

1 Answer
Sam F.
Feb 12, 2018

f(x+h)-f(x)=6xh+3h^2-7hf(x+h)−f(x)=6xh+3h2−7h

Explanation:

f(x+h)-f(x)=3(x+h)^2-7(x+h)+2-(3x^2-7x+2)f(x+h)−f(x)=3(x+h)2−7(x+h)+2−(3x2−7x+2)

f(x+h)-f(x)=3(x^2+2xh+h^2)-7x-7h+2-3x^2+7x-2f(x+h)−f(x)=3(x2+2xh+h2)−7x−7h+2−3x2+7x−2

f(x+h)-f(x)=3x^2+6xh+3h^2+2-3x^2+7x-2f(x+h)−f(x)=3x2+6xh+3h2+2−3x2+7x−2

Simplifying...

f(x+h)-f(x)=6xh+3h^2-7hf(x+h)−f(x)=6xh+3h2−7h

I will say that you would normally see this question asked:

Find (f(x+h)-f(x))/((x+h)-x)f(x+h)−f(x)(x+h)−x

This is the formula associated with finding derivatives in calculus. But if you just need the top (numerator), it is f(x+h)-f(x)=6xh+3h^2-7hf(x+h)−f(x)=6xh+3h2−7h
Just make sure that you are answering the right question!

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