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Из стэнфордского курса Convex Optimization:
How do you, how do you determine if a function from R to R is convex? You plot it, and, and you look with your eyeball: does it curve up or down? Or both, right? And if it curves up then you say, well, it’s convex. OK, by the way, what you do then is you back off and you go to some other fancy method, like, you differentiate it twice and prove some inequality. And then you destroy evidence that you actually plotted it but the correct thing to do is to plot it. Okay, so that, that, that's how you use this. Okay?
How do you, how do you determine if a function from R to R is convex? You plot it, and, and you look with your eyeball: does it curve up or down? Or both, right? And if it curves up then you say, well, it’s convex. OK, by the way, what you do then is you back off and you go to some other fancy method, like, you differentiate it twice and prove some inequality. And then you destroy evidence that you actually plotted it but the correct thing to do is to plot it. Okay, so that, that, that's how you use this. Okay?