Find the maximum rate of change off at the given point and the direction in which it occurs. f(x, y) = 4y √x, (4, 1)

Maximum rate change |f| = √65

Direction = ( 1, 8 ) / √65

i.e Maximum rate change is √65 and it occurs in a direction of ( 1, 8 )

Step-by-step explanation:

Given that;

f(x, y) = 4y √x, (4, 1)

{ x=4 and y=1 }

Maximum rate of change occurs with the gradient vector;

f = [ df/dx, df/dy ] = [ 2y/√x, 4√x ]

we substitute in our value of x and y

f =  2(1)/√4, 4√4

f = 2/√4, 4√4

f = ( 1, 8 )

Maximum rate change |f| = | ( 1, 8 ) | = √( 1² + 8² ) = √(1 + 64)

Maximum rate change |f| = √65

Direction = f / |f|

we substitute

Direction = ( 1, 8 ) / √65

i.e Maximum rate change is √65 and it occurs in a direction of ( 1, 8 )

i believe that is true.

step-by-step explanation:

hope my answer has you if not i'm sorry.

since the airplane is moving with constant speed then the distance travelled can be calculated by x=u*t

in km/h would be:

x=640*3.5=2.240 km

in m/s would be:

u=640 km/h= 640.000 m/h =640.000/ 3600 m/s =177.8 m/s

t= 3.5 h= 3.5 * 3600 s=12.600 s

then x=u*t= 177.8*12.600= 2.240.280 m