(a) The volume V of a growing spherical cell is
V = 4/3pr3,
where the radius is measured in micrometers (1 µm = 10-6m). Find the average rate of change of V with respect to r when r changes from 3 to each of the following. (Round your answers to one decimal place.)
(i) 3 to 6 µm
µm3/µm

(ii) 3 to 4 µm
µm3/µm

(iii) 3 to 3.1 µm
µm3/µm

(b) Find the instantaneous rate of change of V with respect to r when r = 3 µm. (Round your answer to one decimal place.)
V'(3) = µm3 / µm

(i)=263.9 micrometer square

(ii)=155 micrometer square

(ii)=116.9 micrometer square

(b).37.7 micrometer square

Step-by-step explanation:

Given,

Average rate of change  V  with respect to  a to b  where a and b are radius

(i)  3 to 6 micrometer

      micrometer square

(ii)  3 to 4

 micrometer square

(iii) 3 to 3.1

micrometer square

(b) At r=3 micrometer

Instantaneous rate

micrometer square

micrometer square

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.