Difference quotient — Precalculus, what it means and where it is taught
f(x+h)-f(x)h, the slope over a gap of h.
Taught in Precalculus.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Slope — How much y changes for each 1 that x increases.
Practise this idea
2 questions in the course bank use Difference quotient, in Rates of Change & the Derivative.
Problem 1
Simplify the difference quotient (x+h)2-x2h.
Worked answer
2x+h
2xh+h2h
= 2x+h
Problem 2
Using the difference quotient, find f'(x) for f(x)=x2.
Worked answer
2x
The quotient simplifies to 2x+h
As h → 0 that becomes 2x