For starters the difference quotient is crucial in calculus since it is like a part of the semester and it is also known as the derivative. The derivative is the slope of all tangent lines on the graph. When using it, we can determine the possible slopes on various graphs. Secant lines are lines that will touch the graph twice but tangent lines are lines that will touch the graph at only one point. H and delta x are variables for the derivative and on a graph, y-value is your f(x) and the x-value is your h or delta x. For derivatives, the thing to add on is that we aren't only finding the difference quotient but we're also determining h as it approaches 0. From here we can do various things like find the tangent slope or the tangent line or any specific values. The thing to remember the the difference quotient is f(x) but the derivative is f'(x) (f prime of x).
Source
Derivative
Difference Quotient
Secant & Tangent
