Determine whether rolle's theorem applies to the function shown below on the given interval. if so, find the point(s) that are guaranteed to exist by rolle's theorem. f(x)equals=x(xminus−44)squared2; [0,44]

Since the function is continuous between x = 0 and x = 44 then Rolle's theorem applies here.

Differentiating

y' = x * 2(x - 44) + (x - 44)^2

y' = 3x^2 - 176x + 1936 = 0 (at a turning point).

solving we get x = 44 , 14.67

y" = 6x - 176 which is negative for x = 14.67 so this gives a maximum value for f(x)

This maximum is at the point (14.67, 12,619.85)

There is a minimum at ( 44,0)

These are the required points

not enough information

step-by-step explanation:

we cannot know this, because the other students could have handed out 10 flyers, or they could have handed out 100. one way, the mean would go up, and another way, the mean would go down.