At what value does each linear Bernstein polynomial achieve its maximum on the interval ?
Answer: achieves its maximum at .
Answer: achieves its maximum at .
At what value does each quadratic Bernstein polynomial achieve its maximum on the interval ?
Answer: achieves its maximum at .
Answer: achieves its maximum at .
Answer: achieves its maximum at .
At what value does each cubic Bernstein polynomial achieve its maximum on the interval ?
Answer: achieves its maximum at .
Answer: achieves its maximum at .
Answer: achieves its maximum at .
Answer: achieves its maximum at .
Based on the answers you gave above, make a conjecture about the general pattern for where the maxima will exist for Bernstein polynomials of any degree.