From this equation, how do I obtain the final graph?

[broken void]

The last image is what I’ve tried, but I’m struggling to obtain the other zeros/roots of both the first and second derivatives.

Can someone help?

[fallen falcon]

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[rapid holly]

i feel like this has been sent before

[broken void]

Yes. I posted it before but am still struggling

[versed gust]

if you just want to find roots , why don't you just see where the graph intersects x axis?

[broken void]

Well because I need the roots to even get the graph in the first place.

I need to obtain the graph by sketching without a graphing calculator

[versed gust]

hmm

[crude ingot]

Yeah, unfortunately, the exact positions of extrema here can't be determined, as the respective transcendental equations don't have solutions that are expressible in elementary functions.

[broken void]

Okay. So there’s no way to solve it using Calculus methods?

[crude ingot]

No, what I meant is that there's no "easy" analytical expression for extrema. You can still find them numerically, though.

[spare acorn]

There's certainly not "easy" solutions, but I found more equations with the same roots as tan(x) = -x/2