USING DERIVATIVE S IN CURVE SKETCHINGTo Sketch the Graphs of functions using Derivatives.Problem. Consider the function f(x) = 8x - x' whose derivative is f(x)Values of x, f(x) and f^i(x) are given in the following table.= 16x -3x361215|(x) = 8x° -%3!f(x) = 16x – 3xSolve this problem by using the following example on the other picture USING DERIVATIVES IN CURVE SKETCHINGObjective: To sketch the graphs of functions using derivatives.Problem: Consider the function f(x) = 6x -r, whose derivative is f'(x) = 6-2x. Values ofx. f(x), and f'(x) are given in the following table.489.8T) - 6-2 60 - 19 - (x)/2.-2-4.-6Much can be leamed about the graph of f(x) by plotting each point (x. f(x) from the table andthen drawing the tangent to the curve at cach point plotted. The tangent in cach case is the linethrough (x, f(x)) that has stope f'(x). Figure (a) shows a smooth curve drawn through the pointsand having the corresponding tungent lines. The smooth curve is the graph of f(x).r(3) = 0f) <0In figure (a), notice that as x increases, the curve rises whenever f'(x) > 0, and the curve fallswhenever f'(x) < 0. When f'(r) = 0, the curve has a horizontal tangent and f(x) attains itsmaximum value.The observations that we have so far made for polynomial functions are valid for any functionf(x) that has a derivative on an interval 1:1. Iff(x) > 0 on an interval 1, then the graph of f(x) rises as x increases.2. If r(2) < 0 on an interval I, then the graph of f(x) rises as x increases.3. If f'() = 0, then the graph f(x) has a horizontal tangent x = c. The funetion may havea local maximum or minimum value, or neither.

Given: fx=8x2-x3f'x=16x-3x2 To sketch: The graph of the function using derivatives.

To Sketch the Graphs of functions using Derivatives. Problem. Consider the function f(x) = 8x - x' whose derivattve is f(x) = 16x – Values of x, f(x) and fMi(x) are given in the following table. 3x 3 6 12 15 f(x) = &x² - x f(x) = 16x – 3x Solve this problem by using the following example on the other picture

To Sketch the Graphs of functions using Derivatives. Problem. Consider the function f(x) = 8x - x' whose derivattve is f(x) = 16x – Values of x, f(x) and fMi(x) are given in the following table. 3x 3 6 12 15 f(x) = &x² - x f(x) = 16x – 3x Solve this problem by using the following example on the other picture

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.4: Average Rate Of Change Of A Function

Problem 29E: Changing Water Levels The graph shows the depth of water W in a reservoir over a one-year period as...

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