Question

Find a function that has local maxima at (0, 1) and (2, 1) and a local minimum at (1, 0)

Answer 1

f(x) = -1/4 (x⁴) + 3/2 (x²) + 1

Explanation:

One function that satisfies the given conditions is:

f(x) = -1/4 (x⁴) + 3/2 (x²) + 1

This function has local maxima at (0, 1) and (2, 1), and a local minimum at (1, 0).