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#### Petrus

##### Well-known member

- Feb 21, 2013

- 739

I start to derivate it

$f'(x)=\frac{1}{x}+1-4x$

And my next step is to fined critical point but I got problem to solve this equation.

$\frac{1}{x}+1-4x=0$

- Thread starter Petrus
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- Thread starter
- #1

- Feb 21, 2013

- 739

I start to derivate it

$f'(x)=\frac{1}{x}+1-4x$

And my next step is to fined critical point but I got problem to solve this equation.

$\frac{1}{x}+1-4x=0$

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- #2

- Jan 26, 2012

- 4,093

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- #3

Hello Petrus, because you have responded well to $\LaTeX$ tips in the past and use them, I wish to offer you a few here:calculate max and min point of the functuin $\ln(x)+x-2x^2$ in the range $(\frac{1}{6},\frac{3}{2})$...

Instead of using the \$ delimiters, use the $\LaTeX$ button on the toolbar which has the \(\displaystyle \sum\) symbol on it. This will automatically generate the MATH tags for you, which incorporate the \displaystyle command to make your fractions larger.

When you wish to enclose tall expressions such as fractions within parentheses (or other bracketing symbols), use:

\left( \right)

and so the given domain, written as \left(\frac{1}{6},\frac{3}{2} \right) looks like \(\displaystyle \left(\frac{1}{6},\frac{3}{2} \right)\). Doesn't that look better?

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- #4

- Feb 21, 2013

- 739

Indeed! Thanks Mark I will use it now You could also tell me this early heheHello Petrus, because you have responded well to $\LaTeX$ tips in the past and use them, I wish to offer you a few here:

Instead of using the \$ delimiters, use the $\LaTeX$ button on the toolbar which has the \(\displaystyle \sum\) symbol on it. This will automatically generate the MATH tags for you, which incorporate the \displaystyle command to make your fractions larger.

When you wish to enclose tall expressions such as fractions within parentheses (or other bracketing symbols), use:

\left( \right)

and so the given domain, written as \left(\frac{1}{6},\frac{3}{2} \right) looks like \(\displaystyle \left(\frac{1}{6},\frac{3}{2} \right)\). Doesn't that look better?

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- #5

Your $\LaTeX$ has come very far in a short period of time...you are doing very well with it!

Have you managed to find the critical points from the derivative?

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- #6

- Feb 21, 2013

- 739

Now I get \(\displaystyle x_1= \frac{1+\sqrt(17)}{8}\) \(\displaystyle x_2=\frac{1-\sqrt(17)}{8}\) (When I use that latex toolbar my sqrt does not look right, any tips on how I shall do my sqrt?)

and now im suposed to take second derivate and check if the x wealth is positive or negative ( if its possitive that means its a min point)

\(\displaystyle f''(x)=-\frac{1}{x^2}-4\)

With only typing one of them in calculator I get that \(\displaystyle x_1= \frac{1+\sqrt(17)}{8}\) is a max point that means also \(\displaystyle x_2=\frac{1-\sqrt(17)}{8}\) is a min point. I am doing correct so far? and the problem is that my \(\displaystyle x_2=\frac{1-\sqrt(17)}{8}\) is not in the range? Do i got correct?

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- #7

\sqrt{17} gives \(\displaystyle \sqrt{17}\)

This is not because of the toolbar, this is how you should write square roots no matter how you choose to delimit your code.

You have correctly found the roots of the quadratic

So, what you want to do is evaluate the given function (the original, the function you differentiated) at the end-points of the domain AND at the critical value which is within the domain, and take the smallest of these values as the function's absolute minimum and the largest of these as the absolute maximum.

The end-points of the domain and any critical values within that domain are the only places at which absolute extrema may occur for the function on the given domain.

What do you find?

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- #8

- Feb 21, 2013

- 739

and max is \(\displaystyle x=\frac{3}{2}\) and \(\displaystyle y=\frac{14}{3}+\log(\frac{3}{2})\)

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- #9

Also, I suggest using your calculator or our Graph Plotter widget to plot the function on the given domain so that you have an idea of what you should find.

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- #10

- Feb 21, 2013

- 739

I am not suposed to write all those 3 point on my orginal function \(\displaystyle \ln(x)+x-2x^2\)?

Also, I suggest using your calculator or our Graph Plotter widget to plot the function on the given domain so that you have an idea of what you should find.

my crit point: ln((1+sqrt(17))/8)+(1+sqrt(17))/8+2((1+sqrt(17))/8)^2 - Wolfram|Alpha

3/2:ln(3/2)+1/6+2(3/2)^2 - Wolfram|Alpha

1/6: ln(1/6)+1/6+2(1/6)^2 - Wolfram|Alpha

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- #11

In all 3 links you have used \(\displaystyle \ln(x)+x+2x^2\), while in the 3rd link you have also mistakenly used a mixture of values for $x$. Review and correct your inputs to W|A, then see what you get.

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- #12

- Feb 21, 2013

- 739

For some reason i still dont get correct...

In all 3 links you have used \(\displaystyle \ln(x)+x+2x^2\), while in the 3rd link you have also mistakenly used a mixture of values for $x$. Review and correct your inputs to W|A, then see what you get.

max: ln((1+sqrt(17))/8)+(1+sqrt(17))/8-2((1+sqrt(17))/8)^2 - Wolfram|Alpha

min: ln(3/2)+3/2-2(3/2)^2 - Wolfram|Alpha

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- #13

Are you supposed to use decimal approximations, and if so how much precision is required? Please tell me the exact instructions you are given regarding entering your results.

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- #14

- Feb 21, 2013

- 739

Thanks Mark and Jameson!

Are you supposed to use decimal approximations, and if so how much precision is required? Please tell me the exact instructions you are given regarding entering your results.

You both helped me and Mark your guide was so great!I do understand now!

(I did input x and y wealth that was wrong, I was suposed to only input y wealth)

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- #15

By the way, you want to use the word "value" not "wealth." While the two words are closely related, in English wealth is not used to denote the magnitude of a numeric quantity (unless it is monetary).

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- #16

- Feb 21, 2013

- 739

Thanks for correcting me on this thing Indeed I need to improve my english cause if it works good for me ima try studdy outside Sweden Btw do you say calculate the max and min point or do you say Find the max and min point?You are so good about giving feedback and letting those who help you know how things turn out!

By the way, you want to use the word "value" not "wealth." While the two words are closely related, in English wealth is not used to denote the magnitude of a numeric quantity.

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- #17