Someone know how to do this???

Question

mony01 · Answer

attachment

psymon · Answer

So it wants you to get f(-8) and f(8) first. Have you done that part at least?

mony01 · Answer

that's the problem I have I don't know how to solve this: 4-8^2/3

psymon · Answer

That is a 2/3 power, correct?

mony01 · Answer

yeah

psymon · Answer

Well, when you have a fraction exponent, the numerator of the fraction is the power and the denominator is the root. So what that 8^(2/3) says is take 8 to the 2nd power, then take that to the 3rd root. This can be done in either order. YOu may take the 3rd root of 8 first then square it or square it first then take the 3rd root. Either way does not matter

$$8^{2/3} \implies \sqrt[3]{64} \implies 4$$or
$$8^{2/3} \implies 2^{2} = 4$$

mony01 · Answer

oh okay and f(-8) is also 4 right?

psymon · Answer

Correct, since the value ends up being squared, forcing it to be positive either way.

mony01 · Answer

since the equation is 4-8^2/3 would it just be 0

psymon · Answer

Right, it wouldbe 0 for both f(8) and f(-8)

mony01 · Answer

okay and when it says to find all values of c in (-8,8). How would I do that?

psymon · Answer

You need to take the derivative of 4-x^(2/3) (and by the way, an exponent like that should be shown in parenthesis, it looked like it was x squared divided by 3). 

Once you take the derivative, you would find all values of x such that the derivative equals 0.

mony01 · Answer

so its -2/3x^(-1/3)

psymon · Answer

Correct. Which is an issue. 
$$\frac{ -2 }{ 3x^{1/3} }$$There are no values of x which make the function = 0. There are no values of x such that the function = 0. The only values to be found are values that make the function undefined. At x = 0, the derivative is undefined. What this says is that there is a point in the interval of (-8,8) where the function is not differentiable, meaning you cannot even use Rolle's Theorem, this does not satisfy the conditions necessary.

psymon · Answer

Didnt mean to type thefirst sentence twice, lol.

mony01 · Answer

so it does not exist. and the last question asking about Rolle's Theorem is it e.

psymon · Answer

Nah, D. It doesnt contradict Rolle's Theorem because it never satisfied the conditions in the first place. f'(0) does not exist and the function is not differentiable in the interval (-8,8)

mony01 · Answer

thank you so much Psymon!!!!! I got them all right.

psymon · Answer

Awesome ^_^