At what $t$ value does each linear Bernstein polynomial achieve its maximum on the interval $[0,1]$?
Answer: $1-t$ achieves its maximum at .
Answer: $t$ achieves its maximum at .
At what $t$ value does each quadratic Bernstein polynomial achieve its maximum on the interval $[0,1]$?
Answer: $(1-t)^2$ achieves its maximum at .
Answer: $2t(1-t)$ achieves its maximum at .
Answer: $t^2$ achieves its maximum at .
At what $t$ value does each cubic Bernstein polynomial achieve its maximum on the interval $[0,1]$?
Answer: $(1-t)^3$ achieves its maximum at .
Answer: $3t(1-t)^2$ achieves its maximum at .
Answer: $3t^2(1-t)$ achieves its maximum at .
Answer: $t^3$ 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.

You can earn partial credit on this problem.