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

##### 1 Answer

Oct 24, 2015

Use algebra to simplify and evaluate the limit.

#### Explanation:

# = 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

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

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

# = 6x-5#

That's it.