Question

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]

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Answer 1

Answer:

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