Concept explainers
Increasing and decreasing functions Find the intervals on which f is increasing and the intervals on which it is decreasing.
27.
Trending nowThis is a popular solution!
Chapter 4 Solutions
Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (4th Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
University Calculus: Early Transcendentals (3rd Edition)
- Using 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_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_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_forward
- 116. Proof Use the definitions of increasing and decreasing functions to prove that $f(x)=x^{3}$ is increasing on $(-\infty, \infty)$.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_forward5) a function with a domain of (-2, infinity): Consider: Is the function continuous at x=1? If not, what type of discontinuity does the function have at x=1?arrow_forward
- Inspect 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_forwardSpread of an Epidemic During a flu epidemic, the total number of students on a state university campus who had contracted influenza by the xth day was given by N(x) = 5000/1 + 49e−x (x ≥ 0). (a) How many students had influenza initially? (b)Derive an expression for the rate at which the disease was being spread. N'(x) = Prove that the function N is increasing on the interval (0, ∞). Because N'(x) < > = 0 ?for all x in (0, ∞), we see that N is increasing on (0, ∞).arrow_forwardUsing linear approximation to estimate f(3.2)-f(3) for f(x)8/(1+x^2)arrow_forward
- Using analytical methods, find all critical numbers (exact values) of the function.f(x) = 1/(x − 1)^2 −1/x^2arrow_forwardUse 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_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