 Home
 Products
 Integration
 Tutorial
 Barcode FAQ
 Purchase
 Company
print barcode image c# d sin(x 2 ) dx d t tan(t 3 t 2 ) dt d x2 1 dx x 2 + 1 [x ln(sin x)] d s(s+2) e ds in Software
d sin(x 2 ) dx d t tan(t 3 t 2 ) dt d x2 1 dx x 2 + 1 [x ln(sin x)] d s(s+2) e ds QRCode Generator In None Using Barcode maker for Software Control to generate, create QRCode image in Software applications. Reading Quick Response Code In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. d sin(x 2 ) e dx [ln(ex + x)] QR Code ISO/IEC18004 Generation In Visual C#.NET Using Barcode maker for .NET Control to generate, create QR image in .NET framework applications. Create Quick Response Code In .NET Framework Using Barcode maker for ASP.NET Control to generate, create QR Code ISO/IEC18004 image in ASP.NET applications. Foundations of Calculus
Drawing Denso QR Bar Code In Visual Studio .NET Using Barcode printer for .NET Control to generate, create QRCode image in .NET applications. Drawing QR Code In VB.NET Using Barcode encoder for VS .NET Control to generate, create QR Code ISO/IEC18004 image in .NET framework applications. (g) (h) Code 128B Creation In None Using Barcode encoder for Software Control to generate, create Code 128C image in Software applications. Print Barcode In None Using Barcode generator for Software Control to generate, create bar code image in Software applications. 5 Imitate the example in the text to do each of these falling body problems (a) (b) A ball is dropped from a height of 100 feet How long will it take that ball to hit the ground Suppose that the ball from part (a) is thrown straight down with an initial velocity of 10 feet per second Then how long will it take the ball to hit the ground Suppose that the ball from part (a) is thrown straight up with an initial velocity of 10 feet per second Then how long will it take the ball to hit the ground d sin(ln(cos x)) dx d sin(cos x) e dx d ln(esin x + x) dx d arcsin(x 2 + tan x) dx d arccos(ln x ex /5) dx d arctan(x 2 + ex ) dx EAN13 Supplement 5 Encoder In None Using Barcode generator for Software Control to generate, create UPC  13 image in Software applications. Data Matrix Creator In None Using Barcode drawer for Software Control to generate, create Data Matrix 2d barcode image in Software applications. 6 Use the Chain Rule to perform each of these differentiations: (a) (b) (c) (d) (e) (f) Painting EAN / UCC  14 In None Using Barcode drawer for Software Control to generate, create USS128 image in Software applications. UCC  12 Generator In None Using Barcode generator for Software Control to generate, create UPC Symbol image in Software applications. 7 If a car has position p(t) = 6t 2 5t + 20 feet, where t is measured in seconds, then what is the velocity of that car at time t = 4 What is the average velocity of that car from t = 2 to t = 8 What is the greatest velocity over the time interval [5, 10] 8 In each of these problems, use the formula for the derivative of an inverse function to nd [f 1 ] (1) (a) (b) (c) (d) f (0) = 1, f f (3) = 1, f f (2) = 1, f f (1) = 1, f (0) = 3 (3) = 8 (2) = 2 (1) = 40 2 Of 7 Code Generation In None Using Barcode generator for Software Control to generate, create Monarch image in Software applications. Drawing Code 3 Of 9 In Java Using Barcode encoder for BIRT Control to generate, create USS Code 39 image in Eclipse BIRT applications. Applications of the Derivative
Code 3/9 Generator In C# Using Barcode creation for .NET framework Control to generate, create Code39 image in Visual Studio .NET applications. Printing Code 128 Code Set B In None Using Barcode generation for Online Control to generate, create ANSI/AIM Code 128 image in Online applications. 31 Graphing of Functions
Paint Matrix 2D Barcode In Visual C#.NET Using Barcode generation for Visual Studio .NET Control to generate, create 2D Barcode image in .NET framework applications. Decode USS Code 39 In .NET Framework Using Barcode scanner for .NET Control to read, scan read, scan image in Visual Studio .NET applications. We know that the value of the derivative of a function f at a point x represents the slope of the tangent line to the graph of f at the point (x, f (x)) If that slope is positive, then the tangent line rises as x increases from left to right, hence so does the curve (we say that the function is increasing) If instead the slope of the tangent line is negative, then the tangent line falls as x increases from left to right, hence so does the curve (we say that the function is decreasing) We summarize: On an interval where f > 0 the graph of f goes uphill On an interval where f < 0 the graph of f goes downhill See Fig 31 With some additional thought, we can also get useful information from the second derivative If f = (f ) > 0 at a point, then f is increasing Hence the slope of the tangent line is getting ever greater (the graph is concave up) The picture must be as in Fig 32(a) or 32(b) If instead f = (f ) < 0 at a point then f is decreasing Hence the slope of the tangent line is getting ever less (the graph is concave down) The picture must be as in Fig 33(a) or 33(b) Using information about the rst and second derivatives, we can render rather accurate graphs of functions We now illustrate with some examples EXAMPLE 31 Matrix 2D Barcode Creator In VS .NET Using Barcode drawer for ASP.NET Control to generate, create Matrix 2D Barcode image in ASP.NET applications. Barcode Creator In .NET Using Barcode creation for Reporting Service Control to generate, create barcode image in Reporting Service applications. Sketch the graph of f (x) = x 2
Copyright 2003 by The McGrawHill Companies, Inc Click Here for Terms of Use
CHAPTER 3 Applications of the Derivative
Fig 31
Fig 32
Fig 33
SOLUTION Of course this is a simple and familiar function, and you know that its graph is a parabola But it is satisfying to see calculus con rm the shape of the graph Let us see how this works CHAPTER 3 Applications of the Derivative
First observe that f (x) = 2x We see that f < 0 when x < 0 and f > 0 when x > 0 So the graph is decreasing on the negative real axis and the graph is increasing on the positive real axis Next observe that f (x) = 2 Thus f > 0 at all points Thus the graph is concave up everywhere Finally note that the graph passes through the origin We summarize this information in the graph shown in Fig 34

