Find the value of a so that the function fx xeax has a

Question

Question: 1. Find values of a and b so that the function f(x) = x² + ax + b has a local minimum at the point (6, -5).

2. Find the value of a so that the function f(x) = xe^ax has a critical point at x = 3.

3. If m, n ≥ 2 are integers, find and classify the critical points of f(x) = x^m(1 - x)ⁿ.