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6/29/2025, 11:25:05 PM
>>16710509
The fact that you use terms like “slow down”, “accelerate” and “intuition” tells me you’re a physicist taking baby’s first analysis course.
So, in proper language, you’re saying a monotonically decreasing function whose domain is the entire R, or at least some open ray (a,infty), with an everywhere-non-negative second derivative must diverge to -infty.
I don’t even understand your teacher’s counterexample because you have a sum from 1 to n of x^-2, which is just nx^-2, but then you make it a function of n? That would make the second derivative vanish. You need to work on your notation and communication, whether you’re right or wrong. You probably said something incoherent to your teacher, he interpreted it in a way different from yours, and then gave you a different counterexample to an entirely different claim.
The fact that you use terms like “slow down”, “accelerate” and “intuition” tells me you’re a physicist taking baby’s first analysis course.
So, in proper language, you’re saying a monotonically decreasing function whose domain is the entire R, or at least some open ray (a,infty), with an everywhere-non-negative second derivative must diverge to -infty.
I don’t even understand your teacher’s counterexample because you have a sum from 1 to n of x^-2, which is just nx^-2, but then you make it a function of n? That would make the second derivative vanish. You need to work on your notation and communication, whether you’re right or wrong. You probably said something incoherent to your teacher, he interpreted it in a way different from yours, and then gave you a different counterexample to an entirely different claim.
6/13/2025, 10:26:09 AM
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