Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) F(x) = sin(x/2) , [π/2,3π/2] ​

The numbers 3(pi)/2, 5(pi)/2 satisfy the conclusion of Rolle's Theorem

Step-by-step explanation:

1. The function must be continuous.  

Trigonometric functions are continuous.  

2.  It must be true that f(a) = f(b) = 0

For this case sin(pi) = sin(3pi) = 0

3. Therefore by Rolle's Theorem, there exist a point, x, such that f(x) = 0

For this case f(x) = cos(x)

And cos(x) = 0 at x = 3(pi)/2,5(pi)/2

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

for a it would be 24 children.

for b i don't understand the question. is it saying for each individual person they pick 5 reds to 7 greens or is it the whole group. clarify and i hope this can you.

step-by-step explanation: