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How do you use the definition of a derivative to find the derivative of $f(x)=x^2 - 1$ , at c=2?

1 Answer

Jan 23, 2017

$4$

Explanation:

let $x_1=2$

$f'(x)=lim_(x->x_1)(f(x)-f(x_1))/(x-x_1)$

$=lim_(x->2)((x^2-1)-(2^2-1))/(x-2)$

$=lim_(x->2)(x^2-1-3)/(x-2)$

$=lim_(x->2)(x^2-4)/(x-2)$

$=lim_(x->2)((x+2)(cancel(x-2)))/cancel(x-2)$

$=lim_(x->2)(x+2)$

$=2+2=4$

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