Concept explainers
Increasing and decreasing functions Find the intervals on which f is increasing and the intervals on which it is decreasing.
28.
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (3rd Edition)
Glencoe Math Accelerated, Student Edition
Precalculus Enhanced with Graphing Utilities (7th Edition)
Calculus & Its Applications (14th Edition)
Calculus and Its Applications (11th Edition)
- Formula for Maximum and Minimum Values Find the maximum or minimum value of the function. f(x)=3x12x2arrow_forwardRadius of a Shock Wave An explosion produces a spherical shock wave whose radius R expands rapidly. The rate of expansion depends on the energy E of the explosion and the elapsed time t since the explosion. For many explosions, the relation is approximated closely by R=4.16E0.2t0.4. Here R is the radius in centimeters, E is the energy in ergs, and t is the elapsed time in seconds. The relation is valid only for very brief periods of time, perhaps a second or so in duration. a. An explosion of 50 pounds of TNT produces an energy of about 1015 ergs. See Figure 2.71. How long is required for the shock wave to reach a point 40 meters 4000 centimeters away? b. A nuclear explosion releases much more energy than conventional explosions. A small nuclear device of yield 1 kiloton releases approximately 91020 ergs. How long would it take for the shock wave from such an explosion to reach a point 40 meters away? c. The shock wave from a certain explosion reaches a point 50 meters away in 1.2 seconds. How much energy was released by the explosion? The values of E in parts a and b may help you set an appropriate window. Note: In 1947, the government released film of the first nuclear explosion in 1945, but the yield of the explosion remained classified. Sir Geoffrey Taylor used the film to determine the rate of expansion of the shock wave and so was able to publish a scientific paper concluding correctly that the yield was in the 20-kiloton range.arrow_forwardTranslations of graphs: What is the relationship between the graphs of the functions y = f(x) and y = f(x − k) when k > 0?Translations of graphs: What is the relationship between the graphs of the functions y = f(x) and y = f(x) + k when k > 0?arrow_forward
- The function is increasing on the interval(s): The function is decreasing on the interval(s): The function is constant on the interval(s): What is the domain of the function:arrow_forwardUsing rectangles each of whose height is given by the value of the function at the midpoint of the rectangle's base (the midpoint rule), estimate the area under the graph of the following function, using first two and then four rectangles. f(x)=1/x between x=2 and x=6 using two rectangles, the estimate for the area under the curve is ___. (round to three decimal places as needed) using four rectangles, the estimate for the area under the curve is ___. (round to three decimal places as needed)arrow_forwardDomain,Interval of growth and decrease ,Asymptote by making the link with the characteristics of f(x) and g(x)arrow_forward
- h(x) = 4/((x-1)^2) Show from the definition that the function h(x) = 4/((x-1)^2) is increasing in the interval (-∞, 1) and decreasing in the interval (1,+∞).arrow_forwardhelppp Increasing on the interval(s) = Decreasing on the interval(s) = Constant on the interval(s) =arrow_forwardInspect the graph of the function to determine whether it is increasing or decreasing on the given interval. f(x)=−3+x on (0,∞) Choose the correct answer below. A. The function is increasing on (0,∞) because its graph is a curve that rises from left to right. B. The function is increasing on (0,∞) because its graph is a curve that lies mostly above the x-axis. C. The function is decreasing on (0,∞) because its graph is a curve that lies mostly below the x-axis. D. The function is decreasing on (0,∞) because its graph is a curve that falls from left to right.arrow_forward
- 116. Proof Use the definitions of increasing and decreasing functions to prove that $f(x)=x^{3}$ is increasing on $(-\infty, \infty)$.arrow_forwardComposite Functions: What does (f*g^(-1))(x) and (g^(-1)*f)(x) stand mean, how do you solve them?arrow_forwardUsing the First Derivative Test Consider the function ƒ(x) = 3x4 - 4x3 - 6x2 + 12x + 1.a. Find the intervals on which ƒ is increasing and those on which it is decreasing.b. Identify the local extrema of ƒ.arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt