Final answer:
To find the maximum value of fs(x), we need to find the critical points and evaluate the function.
Step-by-step explanation:
To find the maximum value of the function fs(x) = (d-x)(a^(1/2)x^b) on the interval 0 < x < 1, we first need to find the critical points by taking the derivative and setting it equal to zero. Differentiating fs(x) with respect to x gives us fs'(x) = b(a^(1/2)x^b-1)(d-x) - x(a^(1/2)x^b) = b(a^(1/2)x^b-1)(d-x) - ax^(b+1/2). Setting this equal to zero, we have b(a^(1/2)x^b-1)(d-x) - ax^(b+1/2) = 0.
After finding the critical points, we need to evaluate the function at the critical points and endpoints to determine the maximum value. Plugging in the critical points into the original function, we can compare the values to find the maximum. However, we need more information about the values of a, b, and d to provide a specific answer.
Therefore, without the values of a, b, and d, we cannot determine the maximum value of fs(x) on the interval 0 < x < 1.