The ideas of "increasing" or "decreasing" have to do with the sign of the derivative of a function. The derivative of a function is a limit, which is only defined if the point can be approached from both sides. For a function that is only defined on an interval, the derivative is undefined (hence "increasing" or "decreasing" are undefined) at the end points of the interval.

When the function is defined on an interval, "increasing" or "decreasing" can only be determined on that open interval. There may also be critical points within an interval at which the derivative is either zero or undefined. Those points must also be excluded from any interval of "increasing" or "decreasing".

If a function is defined over a domain that extends beyond the interval of interest, then the derivative may very wll be defined a the end points of the interval of interest. As a simple example, consider a line with defined non-zero slope: y = kx, k≠0. For k>0, the line will be increasing everywhere. The slope is defined at the end points of any finite interval, so the function can be said to be "increasing" on the closed interval.

Similarly, if the (finite) interval of interest includes the vertex of a parabola defined for all real numbers, the function will be "increasing" on one side of the vertex, and "decreasing" on the other side. Both the "increasing" and "decreasing" intervals will be half-open intervals. The point at the vertex will not be included in either of them.

6 0

3 years ago

What does a path become a circuit and a cycle

Afina-wow [57]

Answer:

We do not travel to the same vertex twice (or more). A cycle is a closed path. ... Different books have different terminology in some books a simple path means in which none of the edges are repeated and a circuit is a path which begins and ends at same vertex,and circuit and cycle are same thing in these books.

Step-by-step explanation:

7 0

3 years ago

What would be the expression?

Gala2k [10]

6*6-(3*3)-(2*2) is the answer

7 0

3 years ago