Need Help?Read It can be applied to fon the closed interval ta, b]. (Select all

Question

Need Help?Read It can be applied to fon the closed interval ta, b]. (Select all that apply.) ] Determine whether Rolle's rx)-7 sin x, [0, 2 Yes, Rolle's Theorem can be applied. a No, because fis not continuous on the closed interval [a, b]. No, because fis not differentiable in the open interval (a, b). No, because (a) fb). If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that fc) o as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.) . (Enter your answers to a 1/2 T6 4.2018 Notes O Ask Your T Determine whether Rolle's Theorem can be applied to f on the dosed interval [La, b]. (Select all that apply.) f(x) 3 cos 2x, [-,m Yes, Rolle's Theorem can be applied.

Explanation / Answer

Answer :

Consider the function

f(x)=7sin(x) and the interval is [ 0 , 2pi ]

Then f'(x) = 7cos(x)

(a) f is continuous on the closed interval [ 0 , 2pi ]

(b) f is differentiable on the open interval ( 0 , 2pi )

(c) f(0) = 7sin(0) = 0 and f(2pi) = 7sin(2pi) = 0

That is f(0) = f(2pi)

Since f is satisfying all the above three conditions. So Rolles theorem can be applied.

By Rolles theorem, there exists at least one value c of x in the open interval ( 0 , 2pi ) such that f'(c) = 0.

That is 7cos(c) = 0 implies that cos(c) = 0 implies that c = pi/2

in ( 0, 2pi )

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