Question

 

part 1)

Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 16 ft high? The height is increasing at ft/min.

part 2)

A conical water tank with vertex down has a radius of 8 feet at the top and is 11 feet high. If water flows into the tank at a rate of 30 ft3/minft3/min, how fast is the depth of the water increasing when the water is 7 feet deep?

The depth of the water is increasing at  ft/min.

part 3)

Find the partial derivatives of the function f(x,y)=−3xy+3y^3+6

fx(x,y)=

fy(x,y)=

part 4)

Find the partial derivatives of the function f(x,y)=−3x^4y^3+5

fx(x,y)=

fy(x,y)=

part 5)

Find the partial derivatives of the function f(x,y)=e^(5x−4y)

fx(x,y)=

fy(x,y)=

Answer 1