#2- for the curve given by 4x2+y2=48+2xy show that
dy/dx=y-4x/y-x

#3- for the curve given by 4x2+y2=48+2xy, find the positive y coordinate given that the xcoordinate is 2.

#4- for the curve given by 4x2+y2=48+2xy, show that there is a point p with x-coordinate 2 at which the line tangent to the curve at p is horizontal.

Step-by-step explanation:

A. The given curve is:

Hence proved.

B. The given curve is:

Put x=2, we get

Thus, y=-4,8

C. The given curve is:

To show point P with x-coordinate 2 at which the line tangent to the curve at P is horizontal, consider

⇒

⇒

At y=8,

⇒8=4x

⇒x=2

The equation of the tangent is:

y-8=0(x-2)

⇒y=8.

Thus, at (2,80, therefore with  x-coordinate 2 the line tangent to the curve at P is horizontal.

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,