# Differential calculus maximum and minimum problem

### Maxima and minima physics

The task is made easier by the availability of calculators and computers, but they have their own drawbacks—they do not always allow us to distinguish between values that are very close together. When looking for local maximum and minimum points, you are likely to make two sorts of mistakes: You may forget that a maximum or minimum can occur where the derivative does not exist, and so forget to check whether the derivative exists everywhere. At the same moment car A begins moving north at 60 mph. Express the product as function of a single variable, and find its maximum. Many students find these problems intimidating because they are "word" problems, and because there does not appear to be a pattern to these problems. Show, in fact, that that area will be 2r2. No maximum or minimum even though the derivative is zero. Click HERE to return to the original list of various types of calculus problems.

Theorem 5. They illustrate one of the most important applications of the first derivative. Do the problem yourself first! The function that is to be minimized is the surface area S while the volume V remains fixed at cubic inches Figure 1.

For convenience, call the product something. At the same moment car A begins moving north at 60 mph. Find the dimensions of the triangle with the shortest hypotenuse. We can perform the same test on the right.

The function, together with its domain, will suggest which technique is appropriate to use in determining a maximum or minimum value—the Extreme Value Theorem, the First Derivative Test, or the Second Derivative Test.

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