Calculus (Cliffs Quick Review) by Bernard V. Zandy, Jonathan J. White

By Bernard V. Zandy, Jonathan J. White

By way of pinpointing the things you really want to grasp, not anyone does it higher than CliffsNotes. This quick, potent instructional is helping you grasp center Calculus ideas -- from services, limits, and derivatives to differentials, integration, and certain integrals -- and get the absolute best grade.
At CliffsNotes, we're devoted to assisting you do your top, regardless of how difficult the topic. Our authors are veteran academics and proficient writers who understand how to chop to the chase -- and nil in at the crucial details you must be triumphant.

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These results agree with the local extrema determined in Example 4-11 using the First Derivative Test on f (x) = – sin x – cos x on [0,2π]. F 4/25/01 8:59 AM Page 51 Chapter 4: Applications of the Derivative 51 Concavity and Points of Inflection The second derivative of a function may also be used to determine the general shape of its graph on selected intervals. A function is said to be concave upward on an interval if f"(x) > 0 at each point in the interval and concave downward on an interval if f"(x) < 0 at each point in the interval.

E5-x – tan x 4. 3 5. F 4/25/01 8:58 AM Page 43 Chapter 4 APPLICATIONS OF THE DERIVATIVE Chapter Check-In ❑ Using the derivative to understand the graph of a function ❑ Locating maximum and minimum values of a function ❑ Finding velocity and acceleration ❑ Relating rates of change ❑ Approximating quantities by using derivatives he derivative of a function has many applications to problems in calculus. It may be used in curve sketching; solving maximum and minT imum problems; solving distance; velocity, and acceleration problems; solving related rate problems; and approximating function values.

The technique of implicit differentiation allows you to find the derivative of y with respect to x without having to solve the given equation for y. The chain rule must be used whenever the function y is being differentiated because of our assumption that y may be expressed as a function of x. dy Example 3-19: Find dx if x 2 y 3 - xy = 10. F 38 4/25/01 8:57 AM Page 38 CliffsQuickReview Calculus Example 3-20: Find y' if y = sin x + cos y. Differentiating implicitly with respect to x, you find that 1 $ y l= cos x - sin y $ y l 1 $ y l+ sin y $ y l= cos x y l(1 + sin y) = cos x cos x y l= 1 + sin y Example 3-21: Find y' at (–1,1) if x2 + 3xy +y2 = –1.

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