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How do you use the definition to find the derivative of $3 x^{2} - 5 x + 2$ $3x^2-5x+2$ ?

1 Answer

Oct 15, 2015

$6 x - 5$ $6x-5$

Explanation:

Let $f (x) = 3 x^{2} - 5 x + 2$ $f(x)=3x^2-5x+2$

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

$=lim_(h->0)((3(x+h)^2-5(x+h)+2)-(3x^2-5x+2))/h$

$=lim_(h->0)(3x^2+6xh+3h^2-5x-5h+2-3x^2+5x-2)/h$

$=lim_(h->0)(h(6x+3h-5))/h$

$=6x-5$

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