Question

write the maximum necessary condition for the following ​

Answer 1

Answer:

local maximum (or minimum) of a function is a point inside the domain in which our function takes a value greater than its value on its neighbors.

A point q at which f has non-zero directional derivative in any direction in which we can move both forward and back, cannot be a maximum or minimum, since moving in that direction from q forward and back will cause f to increase one way and decrease in the other.

The basic condition for an interior "extremum" at point q of a differentiable function f is then that f have zero derivative in every direction that you are allowed to move from q while obeying the conditions on your problem.

For a function of one variable this is just the condition that f ' = 0 at x = q , which is to say that q is a critical point for f .

To find whether f has a maximum or minimum at a critical point you must look to the quadratic approximation (or if necessary to the first higher approximation at which f deviates from flatness) to f . If its second derivative is positive then, like x 2 , f has a minimum at q , and if it is negative f has a maximum.

You should always check whether any local maximum or minimum that you find is the "global" maximum or minimum of f . That global extreme point (or any such points) can occur on a boundary, or at a different local extremum from the first one you find.

If f is a function of several variables then strange things can go on even in the quadratic approximation, and q being a critical point does not imply that it is a maximum or minimum even when the quadratic approximation is far from

Answer 2

a) A trapezium is NOT a parallelogram because a parallelogram have 2 pairs of parallel sides. But a trapezium only has 1 pair of parallel sides.

b) A rectangle has two pairs of opposite sides parallel, and four right angles. It is also a parallelogram, since it has two pairs of parallel sides. A square has two pairs of parallel sides, four right angles, and all four sides are equal.

c) A rhombus is a quadrilateral (plane figure, closed shape, four sides) with four equal-length sides and opposite sides parallel to each other. ... All squares are rhombuses, but not all rhombuses are squares. The opposite interior angles of rhombuses are congruent.

d) Concave quadrilaterals are four sided polygons that have one interior angle that exceeds 180 degrees. Another means of determining if a quadrilateral is concave is to check the diagonals, or the line segment that connects non-adjacent vertices.

Hope this help........