Need some quick help on a homework problem

Question

Hey,

Just need some help on a homework problem that I can't seem to figure out.

The volume of a growing cell is given by V(r) = 4/3 pi r^3 where the radius of the cell increases by 1 to 2 micrometers.

(a) Verify the conditions of the Mean Value Theorem & find all radius that satisfy the conclusion of the Mean Value Theorem.

(b) Using part (a) above, does such a radius exist? Why or why not?

Answer 1

V'(r) = [V(2)-V(1)]/(2-1) = (4/3)pi(2^3) - (4/3)pi(1)^3

=32pi/3 -4pi/3 = 28pi/3

V(r)= (4/3)pi(r^3)

V'(r)= 4pi(r^2) = 28pi/3

r^2 = 7/3

r=sqr(7/3) = about 1.53