Find the directional derivative of f ( x , y , z ) = x y + z 3 f(x, y,z)=xy+z3 at the point P = ( 4 , − 7 , − 2 ) P=(4,−7,−2) in the direction pointing to the origin.

has gradient

The derivative of at in the direction of a vector is

In this case, is the vector pointing from to the origin, which is

and has norm

Then the derivative of at in the direction of is

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

probability for j is 1/4

while

a is 1/6