Math Is Fun Forum

I agree with this also, though I don't know how to arrive at the final answer posted above: 1 / (-M)^1/4.  Can you show me how you would solve?

I have tried to solve it this way:

which is different than

I stand corrected.  Your teacher is correct, because with a constant like 4 you already know the sign.  When there is a function with an unknown (such as x), it may be positive or negative and hence the ± sign.  Sorry for the bum steer to begin with.

Hi Anakin,

This is because the square of a negative or positive always results in a positive.

It may help to think of it as:

Thank you, Avon. 

This is how I tried to solve it originally.  Where I get stuck is on the fact that 1/6 < x < 1/2...  Is it that we are choosing 1/6 from that range because it makes the denominator under

the largest possible value, and therefore makes

a smaller value?  Do you believe that there is a reason that the book arbitrarily chose

= 1/6?  When you say to bound x away from 0, is that the reason why?  i.e. an x value that approaches 0 causes the function to increase without bound?

Also, I used this same approach to try to solve the second problem listed in the first post.  The text says that the answer is

.  Does this mean an arbitrary value of 4 was used for

?  If that's the case, do you have any idea why the book wouldn't state the answer as

=

?

Thank you in advance for any insight you can lend to this!

Cheers.

Thank you for helping me, TheDude.

In your solution to the first problem, you mentioned further optimizing

so that it is closer to x.  I am trying to reconcile how my text book arrived at the answer

.

Do you know how the text arrived at this answer?