Find the maximum sustainable harvest of the given function. f(S)=24S^0.25, where S is measured in thousands.
To find the maximum sustainable harvest, we need to first find the derivative of the function f(S) with respect to S:
f'(S) = 24 * 0.25 * S^(-0.75) = 6S^(-0.75)
Next, we need to find the critical points of the function by setting the derivative equal to zero and solving for S:
6S^(-0.75) = 0
S^(-0.75) = 0
1/S^0.75 = 0
1 = 0 (this has no solution)
Since there are no critical points for this function, the maximum sustainable harvest occurs at the limit as S approaches infinity. Therefore, the maximum sustainable harvest for this function is infinity.