How do you use the definition of a derivative to find the derivative of #f(x)=3x+2#?

1 Answer
Dec 7, 2016

Answer:

#f'(x)=(df)/(dx)=3#
(see below for method using the definition of a derivative).

Explanation:

The definition of the derivative of #f(x)# is
#color(white)("XXX")f'(x)=(df)/(dx)= lim_(hrarr0) (f(x+h)-f(x))/h#

For the example #f(x)=3x+2#
#color(white)("XXX")(df)/(dx)= lim_(hrarr0) ((3(x+h)+2)-(3x+2))/h#

#color(white)("XXXXX")=lim_(hrar0) (cancel(3x)+3hcancel(+2)cancel(-3x)cancel(-2))/h#

#color(white)("XXXXXX")=lim_(harrr0) (3cancel(h))/cancel(h)#

#color(white)("XXXXXX")=lim_(hrarr0) 3#

#color(white)("XXXXXX")=3#