Category Archives: Optimization

Finding Extrema of Multivariable Functions

1. Remember for a curve , we have maxima and minima occur whenever (1) What’s the multivariable analog to this notion?

Posted in Calculus, Gradient, Optimization, Vector Calculus | Tagged | 1 Comment

Calculus isn’t useless: When Velociraptors Attack

1. Some critics may sneer calculus is useless. Oh yeah? Well, we can solve this problem: Question: The velociraptor spots you away and attacks, accelerating at from a stand start, up to its top speed of . When it spots … Continue reading

Posted in Applications, Calculus, Differential, Integral, Optimization | 2 Comments

First Derivative Test

Definition. Let be a function. Then a “Local Minima” is a point such that for any in some open interval containing . Likewise a “local maxima” is a point which has for every in some open interval containing . First … Continue reading

Posted in Optimization | 2 Comments

Optimization Example: Area of Rectangle

We have a string of length . It does not stretch. But we want to form a rectangle using this string as its boundary. Moreover we want this rectangle’s area is maximized. What to do? (Spoiler alert: solution below!)

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Optimization (Motivation)

Briefly, we consider the problem when a tangent line to a curve has zero slope. That is, the derivative of the curve is zero at some point. Such a point is called a “critical point” and tells us about extreme … Continue reading

Posted in Optimization | 2 Comments