College Algebra 1st Edition
ISBN: 9781938168383
Author: Jay Abramson
Publisher: Jay Abramson
1 Prerequisites 2 Equations And Inequalities 3 Functions 4 Linear Functions 5 Polynomial And Rational Functions 6 Exponential And Logarithmic Functions 7 Systems Of Equations And Inequalities 8 Analytic Geometry 9 Sequences, Probability And Counting Theory Chapter3: Functions
3.1 Functions And Function Notation 3.2 Domain And Range 3.3 Rates Of Change And Behavior Of Graphs 3.4 Composition Of Functions 3.5 Transformation Of Functions 3.6 Absolute Value Functions 3.7 Inverse Functions Chapter Questions Section3.3: Rates Of Change And Behavior Of Graphs
Problem 1TI: Using the data in Table 1 at the beginning of this section, find the average rate of change between... Problem 2TI: Find the average rate of change of f(x)=x2x on the interval [1,9] . Problem 3TI: Find the average rate of change of f(x)=x2+2x8 on the interval [5,a] in simplest forms in terms ofa. Problem 4TI: Graph the function f(x)=x36x215x+20 to estimate the local extrema of the function. Use these to... Problem 1SE: Can the average rate of change of a function be constant? Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local... Problem 3SE: How are the absolute maximum and minimum similar to and different from the local extrema? Problem 4SE: How does the graph of the absolute value function compare to the graph of the quadratic function,... Problem 5SE: For the following exercises, find the average rate of change of each function on the interval... Problem 6SE: For the following exercises, find the average rate of change of each function on the interval... Problem 7SE: For the following exercises, find the average rate of change of each function on the interval... Problem 8SE: For the following exercises, find the average rate of change of each function on the interval... Problem 9SE: For the following exercises, find the average rate of change of each function on the interval... Problem 10SE: For the following exercises, find the average rate of change of each function on the interval... Problem 11SE: For the following exercises, find the average rate of change of each function on the interval... Problem 12SE: For the following exercises, find the average rate of change of each function on the interval... Problem 13SE: For the following exercises, find the average rate of change of each function on the interval... Problem 14SE: For the following exercises, find the average rate of change of each function on the interval... Problem 15SE: For the following exercises, find the average rate of change of each function on the interval... Problem 16SE: For the following exercises, consider the graph of fshown in Figure 15. 16.Estimate the average rate... Problem 17SE: For the following exercises, consider the graph of f shown in Figure 15. 17.Estimate the average... Problem 18SE: For the following exercises, use the graph of each function to estimate the intervals on which the... Problem 19SE: For the following exercises, use the graph of each function to estimate the intervals on which the... Problem 20SE: For the following exercises, use the graph of each function to estimate the intervals on which the... Problem 21SE: For the following exercises, use the graph of each function to estimate the intervals on which the... Problem 22SE: For the following exercises, consider the graph shown in Figure 16. Estimate the intervals where the... Problem 23SE: For the following exercises, consider the graph shown in Figure 16. Estimate the point(s) at which... Problem 24SE: For the following exercises, consider the graph in Figure 17. 24. If the complete graph of the... Problem 25SE: For the following exercises, consider the graph in Figure 17. 25. If the complete graph of the... Problem 26SE: Table 3 gives the annual sales (in millions of dollars) of a product from 1998 to 20006. What was... Problem 27SE: Table 4 gives the population of a town (in thousand) from 2000 to 2008. What was the average rate of... Problem 28SE: For the following exercises, find the average rate of change of each function on the interval... Problem 29SE: xFor the following exercises, find the average rate of change of each function on the interval... Problem 30SE: For the following exercises, find the average rate of change of each function on the interval... Problem 31SE: For the following exercises, find the average rate of change of each function on the interval... Problem 32SE: For the following exercises, find the average rate of change of each function on the interval... Problem 33SE: For the following exercises, find the average rate of change of each function on the interval... Problem 34SE: For the following exercises, find the average rate of change of each function on the interval... Problem 35SE: For the following exercises, use a graphing utility to estimate the local extrema of each function... Problem 36SE: For the following exercises, use a graphing utility to estimate the local extrema of each function... Problem 37SE: For the following exercises, use a graphing utility to estimate the local extrema of each function... Problem 38SE: For the following exercises, use a graphing utility to estimate the local extrema of each function... Problem 39SE: For the following exercises, use a graphing utility to estimate the local extrema of each function... Problem 40SE: For the following exercises, use a graphing utility to estimate the local extrema of each function... Problem 41SE: The graph of the functionfis shown in Figure 18. Based on the calculator screen shot, the point... Problem 42SE: Let f(x)=1x . Find a number c such that the average rate of change of the functionfon the interval... Problem 43SE: Let f(x)=1x . Find the number b such that the average rate of change off on the interval (2,b) is... Problem 44SE: At the start of a trip, the odometer on a car read 21,395. At the end of the trip, 13.5 hours later,... Problem 45SE: A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the... Problem 46SE: Near the surface of the moon, the distance that an object falls is a function of time. It is given... Problem 47SE: The graph in Figure 19 illustrates the decay of a radioactive substance over t days. Use the graph... Problem 3SE: How are the absolute maximum and minimum similar to and different from the local extrema?
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Concept explainers
give the critical points of f(x,y) = 2x^3 + xy^2 + 5x^2 + y^2. classify each as a local minimum , local maximum or saddle point.
Formula Formula A function f ( x ) is also said to have attained a local minimum at x = a , if there exists a neighborhood ( a − δ , a + δ ) of a such that, f ( x ) > f ( a ) , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a f ( x ) − f ( a ) > 0 , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a In such a case f ( a ) is called the local minimum value of f ( x ) at x = a .
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