How do you find f'(x) using the definition of a derivative for $f(x)=3x^2-5x+2$ ?

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Answer 1 · 2015-10-24T21:58:42

Use algebra to simplify and evaluate the limit.

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

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

$= lim_(hrarr0)((3(x+h)^2-5(x+h)+2)-(3x^2-5x+2))/h$

We can't evaluate the limit by substitution, because we get the indeterminate form $0/0$ .

Simplify algebraically to get

$= lim_(hrarr0)(6xh+3h^2-5h)/h$

We still can't evaluate the limit by substitution, because we still get the indeterminate form $0/0$ . Reduce the fraction.

$= lim_(hrarr0)(6x+3h-5)$

$= 6x-5$

That's it.

$f'(x) = 6x-5$

How do you find f'(x) using the definition of a derivative for f(x)=3x^2-5x+2f(x)=3x^2-5x+2?