# How do you use the limit definition of the derivative to find the derivative of #f(x)=3x-7#?

##### 1 Answer

Dec 15, 2016

#### Explanation:

The definition of the derivative of

# f'(x)=lim_(h rarr 0) ( f(x+h)-f(x) ) / h #

So Let

# \ \ \ \ \ f(x+h) = 3(x+h) -7 #

# :. f(x+h) = 3x+3h -7 #

And so the derivative of

# \ \ \ \ \ f'(x) = lim_(h rarr 0) ( (3x+3h -7) - (3x-7) ) / h #

# " " = lim_(h rarr 0) ( 3h ) / h #

# " " = lim_(h rarr 0) 3 #

# :. f'(x) = 3 #