# How do you find and simplify f(x+h)-f(x) and (f(x+h)-f(x))/h given f(x)=7x^2-1?

Oct 23, 2016

Please see the explanation for the process.

#### Explanation:

Given:
$f \left(x\right) = 7 {x}^{2} - 1$

$f \left(x + h\right) = 7 {\left(x + h\right)}^{2} - 1$

$f \left(x + h\right) = 7 \left({x}^{2} + 2 x h + {h}^{2}\right) - 1$

$f \left(x + h\right) = 7 {x}^{2} + 14 x h + 14 {h}^{2} - 1$

$f \left(x + h\right) - f \left(x\right) = 7 {x}^{2} + 14 x h + 14 {h}^{2} - 1 - \left(7 {x}^{2} - 1\right)$

$f \left(x + h\right) - f \left(x\right) = 14 x h + 14 {h}^{2}$

$\frac{f \left(x + h\right) - f \left(x\right)}{h} = \frac{14 x h + 14 {h}^{2}}{h}$

$\frac{f \left(x + h\right) - f \left(x\right)}{h} = 14 x + 14 h$