Question

can you guys help me with these questions

Which of the following could be the units for dy/dx if y is the surface area of a tumor and x is the radius of the tumor?


square millimeters per millimeter


millimeters per centimeter


meters per second


gallons per hour


meters per radian

Which points on the curve of x2 − xy − y2 = 5 have vertical tangent lines?



(1, −2)


(2, −1) and (−2,1)


(0, squre root of 5)


There are no vertical tangents to this curve.


None of the above

Answer 1

surface area in m^2/radius in meters is meters
radians is arc, no units
so
meters per radian

Answer 2

I assume you mean
x^2 - x y - y^2 = 5

2 x dx - x dy -y dx - 2 y dy = 0

(2y-x)dy = (2x-y)dx

dy/dx = (2x-y)/(2y-x)

slope is undefined (vertical) when
2y-x = 0
or
x = 2y
so
x^2 - x y - y^2 = 5
4y^2 -2y^2-y^2 = 5
y = +/-sqrt 5
then x = +/- 2 sqrt 5