The Lagrangian for this function and the given constraints is

which has partial derivatives (set equal to 0) satisfying

This is a fairly standard linear system. Solving yields Lagrange multipliers of

and

, and at the same time we find only one critical point at

.
Check the Hessian for

, given by


is positive definite, since

for any vector

, which means

attains a minimum value of

at

. There is no maximum over the given constraints.
Answer:
Brother's age = 15
Sister's age = 9
Step-by-step explanation:
This graph will start at (.5, 0) as the vertex.
To find this, all you need to do if find the point where inside the absolute value sign is equal to 0. Since the graph can never have a negative value, this will be the lowest point.
2x - 1 = 0
2x = 1
x = .5
From there, you can plot each point by going up two and to the left one.
Examples of Points: (1.5, 2) and (2.5, 4)
You can also plot the other side of the graph by going up two and to the right one.
These points can be found using the slope, which is the number attached to x (2).
Example of Points (-.5, 2) and (-1.5, 4).
En matemáticas, un conjunto contable es un conjunto con la misma cardinalidad (número de elementos) que un subconjunto del conjunto de números naturales. Un conjunto contable es un conjunto finito o un conjunto contable infinito.