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

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Answer 1 · 2017-09-02T11:34:27

$f(x) =x^2 -x -2 ; f'(x) = 2x -1$

A) Let $f(x) = x^2 ; f^'(x) = lim_(h>0) ((x+h)^2 -x^2)/h$ or

$lim_(h>0) (cancelx^2+2hx+h^2 - cancelx^2)/h$ or

$lim_(h>0) (cancelh(2x+h))/cancelh =2x$ .

B) $f(x) = x ; f^'(x) = lim_(h>0) ((cancelx+h) -cancelx)/h$ or

$lim_(h>0) h/h =1$

C) $f(x) = 2 ; f^'(x) =0$

$f(x) =x^2 -x -2 ; f'(x) = 2x -1$ [Ans]

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