Here's the problem:
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.
3. f(x) = sin2?x, [-1,1]
I know that the answer in the back is (+/-)1/4 and (+/-)3/4 but I cant seem to get that answer. Here's my work:
a. Verify that its continuous - Check
b. Verify that its differentiable - Check -> xcos2? + sin2?
c. Verify that f(a) = f(b) - Check -> -1 = 1 >> sin(-2?) = sin(2?) >> 0 = 0
Now I have to find f'(c) which I keep getting wrong. I get (from step b) xcos2? = -sin2? >> x = (-sin2?/cos2?) >> x = 0.
I keep getting x = 0 but the back of the book says the answer is (+/-)1/4 and (+/-)3/4. Please help me.
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.
3. f(x) = sin2?x, [-1,1]
I know that the answer in the back is (+/-)1/4 and (+/-)3/4 but I cant seem to get that answer. Here's my work:
a. Verify that its continuous - Check
b. Verify that its differentiable - Check -> xcos2? + sin2?
c. Verify that f(a) = f(b) - Check -> -1 = 1 >> sin(-2?) = sin(2?) >> 0 = 0
Now I have to find f'(c) which I keep getting wrong. I get (from step b) xcos2? = -sin2? >> x = (-sin2?/cos2?) >> x = 0.
I keep getting x = 0 but the back of the book says the answer is (+/-)1/4 and (+/-)3/4. Please help me.