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PDF MATH 124–005 Lecture Notes

MATH 124–005 Lecture Notes - Application of derivatives Second Derivative Test for Local Maxima and Minima Suppose p is a critical point of a continuous function f and f0(p) = 0 If f is concave up at p (f00(p) > 0) then f has a local minimum at p If f is concave down at p (f00(p) < 0) then f has a local maximum at p

  • What are the applications of partial derivatives?

    31. Applications of partial derivatives: • Derivatives are constantly used in everyday life to help measure how much something is changing. They're used by the government in population censuses, various types of sciences, and even in economics.. 32. Applications of partial derivatives: • Derivatives in physics.

  • How are derivatives used in a rocket launch?

    In addition, we examine how derivatives are used to evaluate complicated limits, to approximate roots of functions, and to provide accurate graphs of functions. A rocket launch involves two related quantities that change over time. Being able to solve this type of problem is just one application of derivatives introduced in this chapter.

  • What does the first derivative of a function tell us?

    The Shape of a Graph, Part I – In this section we will discuss what the first derivative of a function can tell us about the graph of a function. The first derivative will allow us to identify the relative (or local) minimum and maximum values of a function and where a function will be increasing and decreasing.

  • What are the uses of derivatives in mathematics?

    Derivatives in Mathematics: The most common use of the derivatives in Mathematics is to study functions such as: • Extreme values of function • The Mean Value theorem • Monotonic functions • Concavity & curve sketching • Newton’s Method etc. 22.

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