Help me find the values (max/min/inflection/concavity) please?

[AlmightyOcho]

Hello all, first poster here. This problem has been bugging me a lot in my Calc 1 class. I just can't seem to input/find what I'm supposed to be looking for... I've graphed f(x), f'(x), and f''(x) on desmos but I'm still lost as to what values are what, or perhaps I'm not getting the format correct. I found the increasing/decreasing intervals. Can someone point me in the direction for the values for concavity, local max, & inflection points please?

I've got a chegg study account, I utilize mathway, symbolab, wolfram, etc. So I'm not completely in the dark in this class as they've really helped in understanding some of these problems. I figured I'd turn to this forum to see what you all think. Thank you!

f(x)= x^(2/3)/(5+x+x^4)

 

[Dr.Peterson]

Are you saying you have no idea how to answer those questions, or did you try answers and they were rejected? If you did, what were those answers?

What is your understanding of the meaning of concave up or down? How is it related to the second derivative? And what about inflection points?

How is a local maximum related to the first derivative? I'd think if you can work out where it is increasing or decreasing, you could answer this as well, as it is closely related.

Once we know what you are thinking, we can fill in the gaps. Until then ... I'm in the dark as to what help you need.

 

[AlmightyOcho]

Oddly enough your post simply humbled me enough to do some deep reading back into my textbook. I sketched some sample graphs on desmos and remembered the right CALC functions on my calculator to find my values. Thank you so much, & I mean it. My hectic schedule messes with my thinking sometimes.

 

[Dr.Peterson]

Looks good! Part of our goal is to get students to think for themselves, which is the only way to really learn. You're right that rushing (and technology) can interfere with that.

I would say that it's not just "humbling", but also "enabling" - reminding you that you know enough to do it on your own, and aren't dependent on others.