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

Feb 12, 2018

$f \left(x + h\right) - f \left(x\right) = 6 x h + 3 {h}^{2} - 7 h$

#### Explanation:

$f \left(x + h\right) - f \left(x\right) = 3 {\left(x + h\right)}^{2} - 7 \left(x + h\right) + 2 - \left(3 {x}^{2} - 7 x + 2\right)$

$f \left(x + h\right) - f \left(x\right) = 3 \left({x}^{2} + 2 x h + {h}^{2}\right) - 7 x - 7 h + 2 - 3 {x}^{2} + 7 x - 2$

$f \left(x + h\right) - f \left(x\right) = 3 {x}^{2} + 6 x h + 3 {h}^{2} + 2 - 3 {x}^{2} + 7 x - 2$

Simplifying...

$f \left(x + h\right) - f \left(x\right) = 6 x h + 3 {h}^{2} - 7 h$

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

Find $\frac{f \left(x + h\right) - f \left(x\right)}{\left(x + h\right) - x}$

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