You are here:

Calculus/Calculus

Question
How do you find the simplified form of the difference quotient for the function:

f(x) = ax^4

The difference quotient is just   (  f(x+h)-f(x)   )/h

So just the numerator of the difference quotient f(x+h)-f(x) will yield (if you remember how to expand (x+h) to the 4th power, it is not x^4 + h^4 )

f(x+h)-f(x)  =  a(x+h)^4 -  ax^4
=  a (x^4 + 4 x^3 h + 6 x^2 h^2 + 4 x h^3 + h^4 ) - ax^4
=  a x^4 + 4a x^3 h + 6a x^2 h^2 + 4a x h^3 + ah^4  - ax^4
=  4a x^3 h + 6a x^2 h^2 + 4a x h^3 + ah^4
=  (4a x^3  + 6a x^2 h + 4a x h^2 + ah^3 ) h    (since every term now has an h)

Now I shall leave it to you to divide that by h (do some cancellation and get a final simplified form of the
difference quotient of f(x) = ax^4.

Calculus

Volunteer

Amos

Expertise

I can answer all calculus question. I am a Math Lecturer and I teach Math in a College, usually Calculus 1, Calculus 2 and Calculus 3 and Linear Algebra.

Experience

I have been teaching in this college for more than 12 years. Prior to that, I taught for three years as Visiting Assistant Professor.

Education/Credentials
I got my doctorate from Univ. of Rochester in Algebraic Toppology. I got a MA from Univ of Rochester, an MA from York Univ. in Toronto and almost did my M.Sc in the National Univ. of Singapore.