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How do you find the f'(x) using the formal definition of a derivative if $f (x) = 2 x^{2} - 3 x + 4$ $f(x)= 2x^2 - 3x+4$ ?

1 Answer

Alan P. · Antoine

Apr 12, 2015

$f'(x) = lim_(hrarr0) (f(x+h)-f(x))/h$

For $f(x) = 2x^2-3x+4$
this becomes

$f'(x)$

$= lim_(hrarr0)((2(x+h)^2 -3(x+h) +4) - (2x^2 -3x +4))/h$

$= lim_(hrarr0) (4xh + h^2-3h)/h$

$=lim_(hrarr0) (4x +h -3)$

$= 4x-3$

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