Hello! How do I solve for x in the second item in this min max problem

[flopjacks]

I've tried converting it into product form so that I could use the product rule for derivation, but after it I was lost. Am I doing right?

 

[Otis]

How do I solve … the second [exercise]?

…tried converting it into product form [to] use the product rule … but after [trying] I was lost.

Hi flopjacks. That's a good approach for #2, so what happened? Are you lost because you're not able to complete that conversion? Or, is it because you don't understand how to apply the product rule after expressing y as a product? Or, are you lost at some other stage?

Please follow the forum's posting guidelines (summary) and show how far you got or explain specifically why you're lost. Thank you!

In case you were not able to begin the conversion to a product, here's a hint: The definition of negative exponents tells us that the reciprocal of some quantity B may be expressed as B^-1.

Therefore: A/B = (A)(1/B) = A∙B^-1

PS: Does the instruction to "Find the maximum, minimum or inflection point" mean that you get to choose a single point to report? I'm wondering whether they meant to say "point(s)" and to use the word 'and' instead of 'or' (along with the condition "if they exist"). If you're not sure, then I'd report all of them.
[imath]\;[/imath]

 

[flopjacks]

Hello Otis, thank you for answering my question. I think I am lost in the final stage of the simplification, I got 4(2+x)(2−x)/(x^2+4)^2 and I don't know what to do in order to find the values for x in this fraction form

 

[Harry_the_cat]

Good, your differentiation and simplification is correct.

Stationary points occur when y'=0. I'm sure you know that.

Remember that a fraction equals 0 when the numerator equals 0 (as long as the denominator doesn't).

Does that help you find the value/s of x at stationary points?