How do you use the definition of a derivative to find the derivative of #f(x)=6#?

2 Answers
Mar 4, 2015

The definition of derivative is:

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

So:

#lim_(hrarr0)(6-6)/h=0#.

Mar 4, 2015

The definition of derivative tells you that:
#f'(x)=lim_(Deltax->0)[f(x+Deltax)-f(x)]/(Deltax)# where #Deltax# is an increment of #x# corresponding to an increment of your function #f(x+Deltax)#.
Your function is a constant so you have that:
#f(x)=6#
#f(x+Deltax)=6#
i.e. your function has always the same value, #6#;
You can now write:
#f'(x)=lim_(Deltax->0)[f(x+Deltax)-f(x)]/(Deltax)=#
#f'(x)=lim_(Deltax->0)[6-6]/(Deltax)=0#

hope it helps