Rolle's Theorem does not apply to the function because there are points on the interval (a,b) where f is not differentiable.
Given the function is 
and the Rolle's Theorem does not apply to the function.
Rolle's theorem is used to determine if a function is continuous and also differentiable.
The condition for Rolle's theorem to be true as:
- f(a)=f(b)
- f(x) must be continuous in [a,b].
- f(x) must be differentiable in (a,b).
To apply the Rolle’s Theorem we need to have function that is differentiable on the given open interval.
If we look closely at the given function we can see that the first derivative of the given function is:
![\begin{aligned}f(x)&=\sqrt{(2-x^{\frac{2}{3}})^3}\\ f(x)&=(2-x^{\frac{2}{3}})^{\frac{3}{2}}\\ f'(x)&=\frac{3}{2}(2-x^{\frac{2}{3}})^{\frac{1}{2}}\cdot \frac{2}{3}\cdot (-x)^{\frac{1}{3}}\\ f'(x)&=\frac{-\sqrt{2-x^{\frac{2}{3}}}}{\sqrt[3]{x}}\end](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Df%28x%29%26%3D%5Csqrt%7B%282-x%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%5E3%7D%5C%5C%20f%28x%29%26%3D%282-x%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5C%5C%20f%27%28x%29%26%3D%5Cfrac%7B3%7D%7B2%7D%282-x%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5Ccdot%20%5Cfrac%7B2%7D%7B3%7D%5Ccdot%20%28-x%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5C%5C%20f%27%28x%29%26%3D%5Cfrac%7B-%5Csqrt%7B2-x%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D%7D%7B%5Csqrt%5B3%5D%7Bx%7D%7D%5Cend)
From this point of view we can see that the given function is not defined for x=0.
Hence, all the assumptions are not satisfied we can reach a conclusion that we cannot apply the Rolle's Theorem.
Learn more about Rolle's Theorem from here brainly.com/question/12279222
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Answer:
Step-by-step explanation:
Since the height isn't given, we assume it to be "h" (of cylinders). And the answer will be in terms of "r" and "h".
The area of 1 arm is given, so the area of 2 arms would be:
Now, area of 2 cylinders would be the formula:
So, total area is A_arm PLUS A_cyl. The fractional area the arms are would be gotten by taking expression A_arm divided by A_total.
Shown below:
We simplify further:
THis is the answer.
Answer:
An egg
Step-by-step explanation:
Hope this helps you
Given:
The given digits are 1,2,3,4,5, and 6.
To find:
The number of 5-digit even numbers that can be formed by using the given digits (if repetition is allowed).
Solution:
To form an even number, we need multiples of 2 at ones place.
In the given digits 2,4,6 are even number. So, the possible ways for the ones place is 3.
We have six given digits and repetition is allowed. So, the number of possible ways for each of the remaining four places is 6.
Total number of ways to form a 5 digit even number is:
Therefore, total 3888 five-digit even numbers can be formed by using the given digits if repetition is allowed.
Hi!
Answer:
A) 331.24
Step-by-step explanation:
To find the area, you need to multiply LxW, (Length x Width) and in this case, since it's a square, the sides are equal. Each side is 18.2 cm, so all we have to do is multiply 18.2 by 18.2, and then we get 331.24, so your answer is option A.
I hope this helps! :)
