Concept explainers
Increasing and decreasing functions Find the intervals on which f is increasing and decreasing.
36.
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
Precalculus Enhanced with Graphing Utilities (7th Edition)
Calculus & Its Applications (14th Edition)
Precalculus (10th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
- Adding Functions A certain function f is the sum of two temperatures, one given by t2+3, and the other given by tt2+1. Find a formula for f in terms of t.arrow_forwardS-20 Rational Function Is y=x3+4x2+x+1 is a rational function?arrow_forwardIdentify the intervals where ƒ(x)=(1/4)·x4+(1/3)·x3−8·x2−16·x is increasing and where decreasing on the interval [−4,4]. Then determine the relative extrema of ƒ(x). Lastly, determine the absolute extrema of ƒ(x).arrow_forward
- Use closed interval method to find the absolute max and min values of f(x)= x/(x^2 +2) on the interval -1 less than or equal to x less than or equal to 4. Show work using calculus and round to 2 decimal places if neededarrow_forwardThe 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_forwardA step function assumes a constant value between consecutive integers n and n 1. Make a plot of the step function f +x/ whose value is n2 when n x n 1. Use the domain 0 x 20.arrow_forward
- (1) On what open interval is f 'an increasing function? (2) For which value of x is f '(x) minimum? x= (3) For this value of x, how does the rate of change of f compare with the rates of change of f for other values of x? Explain. The rate of change of f at this value of x is less than or equal to or greater than the rate of change of f for all other values of x.arrow_forwardInspect the graph of the function to determine whether it is increasing or decreasing on the given interval. f(x)=4x+1 on (−∞,∞) Choose the correct answer below. A. The function is increasing on (−∞,∞) because its graph is a line with positive slope. B. The function is decreasing on (−∞,∞) because its graph is a line with positive slope. C. The function is increasing on (−∞,∞) because its graph is a line with a positive y-intercept. D. The function is decreasing on (−∞,∞) because its graph is a line with a positive y-interceparrow_forwardUsing rectangles whose height is given by the value of the function at the midpoint of the rectangle's base, estimate the area under the graph using four rectangles. f(x)=x2 between x=1 and x=2arrow_forward
- Domain,Interval of growth and decrease ,Asymptote by making the link with the characteristics of f(x) and g(x)arrow_forwardh(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_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
- College 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 LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage