Difficulty with functions.

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Phoenix08

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Me and my friend were practicing a mock test. This is a question I have not been taught (the fact that I am not able to speak much Chinese doesn’t help). If someone could talk me through the question and answer and how to do it, I’d appreciate it. According to her:
（1）Finding monotone interval
（2） For any positive number, prove:

If anyone can help me with this, it would be appreciated.
 
Your translation appears to be incomplete. A translation site returned this (excluding the function definition):

1651003214661.png

Now please show us what you have tried, so we have something concrete to discuss.
 
Sorry, I do not speak Chinese so I did not understand it.

Could we start at the beginning? How would we start?

Phoenix08 said:
Sorry, I do not speak Chinese so I did not understand it.

Could we start at the beginning? How would we start?
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I know that we need to work out if it is increasing or decreasing.
 
What method do you suggest?

I know how to do it on simpler questions, but more complex questions are very difficult for me.
 
Phoenix08 said:
I know how to do it on simpler questions, but more complex questions are very difficult for me.
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Are you asking about how to differentiate this, or something else? If you put in some effort, at least in phrasing your questions clearly and showing what you've tried, you'll make much faster progress.

I would express the function in terms of negative fractional powers, which are easier to work with than radicals and fractions.

You may want to set a=8 first to do part (a), which will make it a little easier.
 
Dr.Peterson said:
Are you asking about how to differentiate this, or something else? If you put in some effort, at least in phrasing your questions clearly and showing what you've tried, you'll make much faster progress.

I would express the function in terms of negative fractional powers, which are easier to work with than radicals and fractions.

You may want to set a=8 first to do part (a), which will make it a little easier.
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Sorry for being unclear.

The difficulty I’m having is knowing how to find a derivative because there are fractions and square roots involved. I’ve got very little to show, so I apologise.

I replaced a with 8.

1651020865663.png


Is this correct?
I do not know how to find the last derivative.

I only started studying calculus earlier today, so I apologise if I’m learning slowly.
 
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Rewrite \(\displaystyle \dfrac {1}{\sqrt {1+x}} = \dfrac{1}{(1+x)^{1/2}}\ as\ (1+x)^{-1/2}\)

Now \(\displaystyle \dfrac {d}{dx}(f(x))^n\ =\ n(f(x))^{n-1}f'(x)\)

Now try to find the derivative of your first two terms.
 
Otis said:
Are you self-studying? (I've never seen the chain rule used in a calculus course on day one.)

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Yes. I’m far below the age they typically teach calculus, and my tutor didn’t teach me any of this. I only spent about 2 hours studying calculus with her, so I feel I tried this question much too early. I will try to get better.

I managed to work it out through more learning. The answer sheet confirmed it. I’d never be able to do it without the help of my computer, and this question was only supposed to take 14 minutes. Thank you very much to all who helped me.

Phoenix08 said:
Yes. I’m far below the age they typically teach calculus, and my tutor didn’t teach me any of this. I only spent about 2 hours (15 minutes of calculus) studying with her, so I feel I tried this question much too early. I will try to get better.

I managed to work it out through more learning. The answer sheet confirmed it. I’d never be able to do it without the help of my computer, and this question was only supposed to take 14 minutes. Thank you very much to all who helped me.
Click to expand...
 
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