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#