Ideas For Performance Reviews

I never employed anyone, so I might be off on this. In my experience, companies use performance reviews to evaluate if their employees are eligible for raises and/or promotions. Oftentimes, politics are the deciding factor in such decisions, as in those who are good at the “corporate game” get what they want. Those who are not get what they deserve. I would wager that there may be some better alternatives. …

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Maximum-Minimum Problems With Multiple Variables

A function \(f\) of two variables has a relative maximum at \((a, b)\) if \[f(x, y) \leq f(a, b)\] for all points \((a, b)\) in a region containing \((a, b)\) has a relative minimum at \((a, b)\) if \[f(x, y) \geq f(a, b)\] for all points \((a, b)\) in a region containing \((a, b)\) Determination Let’s imagine a function \(f\) has a relative maximum or minimum value at some point \((a, b)\). …

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Partial Derivatives

Let’s consider the function \(f\) given by \[z = f(x, y) = x^2y^3 + xy + 4y^2\] Suppose that we fix \(y\) at 3. Then \[f(x, 3) = x^2(3^3) + x(3) + 4(3^2)\] Now we havea function of only one variable. Taking the first derivative with respect to \(x\), we have \[54x + 3\] The general idea is that, given a function \(f\) with more two variables, we can consider \(y\) fixed—even without replacing \(y\) with a specific number—and then calculate its derivative with respect to \(x\). …

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Coding Tutorials Are A Scourge

Programming tutorials are a poor way to learn. The older the article, the less you should trust it. It’s likely to be obsolete, needlessly complicated, or misleading. Because technologies, APIs, and library change rapidly, there’s no point in following an old method verbatim. Tutorials are useful when you have an intermediate grasp of the subject matter and you want to see how someone has solved a problem that you can define. …

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Functions of Several Variables

A function of two variables assigns to each input pair \((x, y)\), exactly one output number \(f(x, y)\). If you imagine that a one-product firm produces \(x\) units of its product at a profit of $4 per unit, then its total profit is given by \[P(x) = 4x\] This is a function in one variable. If the firm produces \(x\) unit of one product at a profit of $4 per unit and \(y\) units of a second product at a profit of $6 per unit, then its total profit is a function of the two variables \(x\) and \(y\). …

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