Problem #135
If
p
(
x
) is a quadratic polynomial such that |
p
(
x
)| ≤ 1 for all
x
such that 0 ≤
x
≤ 1, what is the largest that |
p
′(0)| can be?
What if
p
(
x
) is a cubic polynomial?
What if
p
(
x
) is a polynomial of degree
n
?
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