How do you find f'(x) using the definition of a derivative for $f (x) = 2 x^{2} - x + 5$ $f(x)= 2x^2-x+5$ ?

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Answer 1 · 2015-10-17T23:20:03

$f'(x)=4x-1$

The definition of the derivative is

$lim_(h->0) (f(x+h)-f(x))/h$

Proceeding as follows

$lim_(h->0)[[2(x+h)^2-(x+h)+5]-[2x^2-x+5]]/h$

$lim_(h->0)[[2(x^2+2xh+h^2)-x-h+5]-[2x^2-x+5]]/h$

$lim_(h->0)(2x^2+4xh+2h^2-x-h+5-2x^2+x-5)/h$

$lim_(h->0)(4xh+2h^2-h)/h$

$lim_(h->0)(h(4x+2h-1))/h$

$lim_(h->0)4x+2h-1=4x+2(0)-1=4x-1$

How do you find f'(x) using the definition of a derivative for f(x)= 2x^2-x+5f(x)=2x2−x+5f(x)= 2x^2-x+5?