Suppose that 𝑢 is differentiable, and 𝑢(3) = 10 is a global maximum. What is 𝑢′(0)?

Answer 1

u(3) = 10 is a global maximum It's like a downward opening parabola or other even degreed polynomial

u'(3) = 0

u"(3)< 0 it's concave downward at x=3

u'(0) probably does not = 0 although it might if it is a local max but less than u=10

x=3 could be the axis of symmetry, then u(0) = u(3-3) = u(3+3) = u(6) and u'(0) = -u'(6)

Maybe someone else has more insights. On first reaction, this is about it for me. Interesting problem. But I suspect there's more info in the problem than given. Maybe a 3rd u or u' equation or u" equation.