To find f(x+h) and the difference quotient of f and simplify. Given: P

Jaden Easton

Jaden Easton

Answered question

2021-09-19

To find f(x+h) and the difference quotient of f and simplify.
Given: f(x)=1x3

Answer & Explanation

Elberte

Elberte

Skilled2021-09-20Added 95 answers

Formula used:
a) Identity: (a+b)3=a3+3a2b+3ab2+b3
b) To find f(x+h) we shall plug x+h in the function
c) Difference quotient =f(x+h)f(x)h
Calculations:
a) We have f(x)=1x3. To find f(x+h) we plug (x+h) in place of x.
So f(x+h)=1(x+h)3
f(x+h)=1(x3+3x2h+3xh2+h3). Using identify
Distributing negative with (x3+3x2h+3xh2+h3), we get
f(x+h)=1x33x2h3xh2h3
b) We know the formula to find the difference quotient is f(x+h)f(x)h.
Substituting the values of f(x)=1x3 and f(x+h)=1x33x2h3xh2h3, we get
Difference Quotient
=(1x33x2h3xh2h3)(1x3)h
Distributing the negative with (1x3), we get
=1x33x2h3xh2h31+x3h
Simplifying we get,
=3x2h3xh2h3h
Factoring h, we get
=h(3x23xhh2)h
=3x23xhh2
Conclusion:
For the given

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?