Tissue culture in modelling form?

Question

The rate of change of the area affected by a culture is determined by the form dA/dt = k (A^1/2) (M - A) where the rate is proportional to the number of cells on the periphery (A^1/2) and the unaffected area (M - A). k is the proportionality constant.

How do you prove that the tissue culture is growing fastest when M/3? 2nd derivative = 0? But it doesn't turn up.

Find A(t) in terms of the initial area Ao = A(0)?

After what time does the tissue reach M/2?

Answer 1

You want to show that the first derivative is maximized when its derivative -- aka the second derivative of the original function -- is zero?

Well, one way would be to show that its second derivative -- i.e., the third derivative of the original function -- is negative ...