Hello, I have a question regarding difference quotients. I haven't been able to find a single example of a difference quotient to an exponent higher than 3, so I was hoping someone here could give me a hand.
The exact wording is:
Let f(x) = 2x^5-3x^2+1
What is the difference quotient f' of f?
I solved it to the best of my knowledge, but the answer is rather long which causes me to doubt it. Any thoughts?
you are correct. the answer would be rather lengthy.
f(x)=2x^5-3x^2+1
f(x+h)=2(x+h)^5-3(x+h)^2+1
f'(x)=lim h->0 f(x+h)-f(x)/h
u will have to expand (x+h)^5 using binomial theorem which makes the problem lengthy. at last h would get cancelled. and u will get f'(x)=10x^4-6x
which is nothing but the differentiation of f(x).