Question

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

Answer 1

`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`