How do you find and simplify $f (x + h) - f (x)$ $f(x+h)-f(x)$ and $\frac{f (x + h) - f (x)}{h}$ $(f(x+h)-f(x))/h$ given $f (x) = 7 x^{2} - 1$ $f(x)=7x^2-1$ ?

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Answer 1 · 2016-10-23T14:55:42

Please see the explanation for the process.

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

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

$f (x + h) = 7 (x^{2} + 2 x h + h^{2}) - 1$ $f(x + h) = 7(x^2 + 2xh + h^2) - 1$

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

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

$f (x + h) - f (x) = 14 x h + 14 h^{2}$ $f(x + h) - f(x) = 14xh + 14h^2$

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

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

How do you find and simplify f(x+h)−f(x)f(x+h)-f(x) and f(x+h)−f(x)h(f(x+h)-f(x))/h given f(x)=7x2−1f(x)=7x^2-1?