difference quotient

Question

Find the difference quotient f(x+h)-f(x)/h for the function and simplify it.

f(x)=21x 

The difference quotient is ____. 

Answer 1

Hi Laura,

 

All that is needed to start is to substitute the value of f(x) into the difference quotient formula of  f(x+h)-f(x)/h

 

Substituting 21x for f(x) and 21(x+h)  for f(x+h) into the difference quotient formula yields:

 

(21(x+ h) -21x)÷h

 

distributing the 21 yields:

 

(21x + 21h - 21x)÷h

 

Note that the 21x is canceled by the -21x leaving:

 

21h÷h

 

which simplifies to 21

 

Note that the difference quotient is the same as the derivative. 

 

Answer 2

f(x+h) = 21(x+h) 

difference quotient  = [21(x+h) -21x]/h = [21x+21h-21x]/h = 21h/h = 21