For the standard minimization linear program, the constraints are of the form ax+by≥c, as opposed to the form ax+by≤c for the standard maximization problem. As a result, the feasible solution extends indefinitely to the upper right of the first quadrant, and is unbounded.

If a sequence is not bounded, it is an unbounded sequence. For example, the sequence 1/n is bounded above because 1/n≤1 for all positive integers n. It is also bounded below because 1/n≥0 for all positive integers n. Then it is not bounded above, or not bounded below, or both.

An unbounded solution of a linear programming problem is a situation where objective function is infinite. A linear programming problem is said to have unbounded solution if its solution can be made infinitely large without violating any of its constraints in the problem.

A linear program is infeasible if its feasibility set is empty; otherwise, it is feasible. A linear program is unbounded if it is feasible but its objective function can be made arbitrarily “good”.

Unbounded Feasible Regions An unbounded feasible region can not be enclosed in a circle, no matter how big the circle is. If the coefficients on the objective function are all positive, then an unbounded feasible region will have a minimum but no maximum.

A bounded anything has to be able to be contained along some parameters. Unbounded means the opposite, that it cannot be contained without having a maximum or minimum of infinity.

A solution region of a system of linear inequalities is A solution region of a system of linear inequalities is bounded if it can be enclosed within a circle. If it cannot be enclosed within a circle, it is unbounded.

If the graph is approaching the same value from opposite directions, there is a limit. If the limit the graph is approaching is infinity, the limit is unbounded. A limit does not exist if the graph is approaching a different value from opposite directions.

In theory, you can go on counting forever without ever reaching a largest number. However, infinity can be bounded, too, like the infinity symbol, for example. You can loop around it an unlimited number of times, but you must follow its contour—or boundary.

The corner points are the vertices of the feasible region. Once you have the graph of the system of linear inequalities, then you can look at the graph and easily tell where the corner points are. Notice that each corner point is the intersection of two lines, but not every intersection of two lines is a corner point.

Cusps and corners are points on the curve defined by a continuous function that are singular points or where the derivative of the function does not exist. A corner is, more generally, any point where a continuous function’s derivative is discontinuous. …

A continuous function doesn’t need to be differentiable. There are plenty of continuous functions that aren’t differentiable. Any function with a “corner” or a “point” is not differentiable.

In the same way, we can’t find the derivative of a function at a corner or cusp in the graph, because the slope isn’t defined there, since the slope to the left of the point is different than the slope to the right of the point. Therefore, a function isn’t differentiable at a corner, either.

A function is not differentiable at a if its graph has a corner or kink at a. As x approaches the corner from the left- and right-hand sides, the function approaches two distinct tangent lines.

The limit is what value the function approaches when x (independent variable) approaches a point. takes only positive values and approaches 0 (approaches from the right), we see that f(x) also approaches 0. itself is zero! exist at corner points.

1. Look for points where the derivative has a limit of ∞ (or a limit of −∞).
2. Also if it’s left and right derivatives at a point don’t match then it doesn’t have a derivative there.
3. @Bye_World by the definition of “cusp” that I’m used to, y=|x| wouldn’t qualify.

The instantaneous rate of change is the change in the rate at a particular instant, and it is same as the change in the derivative value at a specific point. For a graph, the instantaneous rate of change at a specific point is the same as the tangent line slope. That is, it is a curve slope.

The instantaneous rate is the rate of a reaction at any particular point in time, a period of time that is so short that the concentrations of reactants and products change by a negligible amount. The initial rate is the instantaneous rate of reaction as it starts (as product just begins to form).

The instantaneous rate of change is the change at that particular moment or the gradient at that point. The key difference between the two is that the average rate of change is over a range, while the instantaneous rate of change is applied at a particular point.

(a) Let h represent the change in x (time) from 1 to. Then the corresponding. change in f(x) (height) is. The average velocity is the change in height divided by the change in time. (b) The instantaneous velocity V is the limit of the average velocity as h approaches 0.

The value of. f(a+h)−f(a)h. is the slope of the line through the points (a,f(a)) and (a+h,f(a+h)), the so called secant line.

The instantaneous rate of change is the slope of the tangent line at a point. A derivative function is a function of the slopes of the original function.