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     satisfy the conclusion of Rolle's Theorem

Step by step.

1. The function must be continuous.

Trigonometric functions are continuous.

2.  It must be true that

For this case      

3. Therefore by Rolle's Theorem, there exist a point     such that .

For this case    

And          at      

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40