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Say we have an inequality that says that ##f(x, y)>c## where ##f(x, y)## is a function of two variables and ##c## is a constant. Assume that we know this inequality to be true when ##x=a## and ##y=b##. If you show that the partial derivatives of ##f(x, y)## with respect to ##x## and ##y## are both greater than zero, does that prove that ##f(x, y)>c## whenever ##x## is greater than or equal to ##a## and ##y## is greater than or equal to ##b##?

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# Proving An Inequality

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