find a function based on the derivative.

Question

What is the formula for V, the volume of a sphere of radius r? Find dV/dr. What is the geometrical meaning of dV/dr?

 

So for this I don't know how to find the function, and without that I cant find the derivative.

The geometric interpretation is like the slope of the secant line for a derivative function right? but I don't know how to apply that either.

 

please help me understand this problem because I am really confused. If you could go step by step, because I struggle sometimes following thought processes pertaining to derivatives. Thank you in advance.

Answer 1

The volume for sphere is

 

V = (4/3)πr³

 

 

dV/dr  means to take the derivative of the volume, V, with respect to the radius, r.

 

 

FYI:  Derivative is slope of tangent line.  Not secant.