Arumor spreads through a school according to the differential equation dy/dt= 3y(0.5-y). what percentage of the school has heard the rumor when it is spreading the fastest?
a.75
b.50
c.25

so.. notice, the derivative is a quadratic with a negative coefficient
on the leading term,
that means, is a parabola opening downwards, it only has one
extrema, a maximum point, at its vertex,

what's the derivative at the vertex? well, is a horizontal tangent line,
thus, slope is 0, so, if you set the derivative to 0, you'll get the
maximum point, or, the peak of the rate for the rumor,

so, what the dickens is "y" at that point?
well

The question is kind of confusing. if it's asking how many variations of answers can you give. then do 4^5 for your answer.this would be something like the first question could be a and the 2nd c or first b next c etc. if you can, ask the teacher for a better confirmation of what it's asking. if i'm assuming correctly what it's asking, it's 625 different variations.