Intervals on Which a Function Is Increasing or Decreasing In Exercises 11-22, find the open intervals on which the function is increasing or decreasing.
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Chapter 4 Solutions
Calculus: Early Transcendental Functions
- Part III: Numerical Derivation Use Numerical derivation to show which of the following functions is the result of the derivation of the function In(cos(x²): Explain. • 2ln(cos(x)) • sin (2x)/cos (x²) • -2x tan(x²)arrow_forwardDistance between cars At noon, car A is 10 feet to the right and 20 feet ahead of car B, as shown in the figure. If car A continues at 88 ft/sec (or 60 mi/hr) while car B continues at 66 f/sec (or 45 mi/hr), express the distance d between the cars as a function of t, where t denotes the number of sec- onds after noon. Exercise 78arrow_forwardUsing calculus, show that |sin x − cos x| ≤ √2 for all x.arrow_forward
- Tutorial Exercise Determine where the function is concave upward and where it is concave downward. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) f(x) = 3x4 - 36x3 + x – 4 Part 1 of 6 We use the ---Select--- Notice that the domain of f is (Enter your answer using interval notation.) First, find the first and second derivatives of f(x) = 3x – 36x3 + x – 4. f'(x) = f"(x) = Submit Skip (you cannot come back)arrow_forwardApproximate the fixed point of the function to two decimal places. [A fixed point xo of a function f is a value of x such that f(xo) = xo.] (x) = cos x Part 1 of 4 A fixed point xo of a function f is a value of x such that (xo) = x0. To approximate the fixed point of the function x) - cos x, let g(x) = r(x) – x = COs(x) X. COS r Differentiate g(x) with respect to x. 9 '(x) =-sinx 1 sin r Part 2 of 4 To approximate the fixed point of function f, approximate a zero of g(x) = cos x - x. The iterative process of Newton's Method is given by the formula, cos Xn - Xn 9(xn) 9 '(Xn) Xn + 1 = Xn - = Xn - x, +1 - 1 sin an = Xn + COS Xn - Xp COs I. sin x, + 1 sin a Part 3 of 4 For n- 1, let x = 1.0. Now calculate the iterations and enter the values in the table below. (Round your answers to four decimal places.) g(xn) 9 '(Xn) 9(xn) g(xn) Xn - 9 (Xp) ) ("x), 6 1 1.0000 -0.4597 -1.8415 0.2496 0.7504 2 0.7504 -0.0190-1.6819 0.0113 3 0.0000 -1.6736 0.0000arrow_forwardSubject: algebraarrow_forward
- Graphical Reasoning In Exercises 65-68, find a and d for the function fx=acosx+d such that the graph of f matches the figure.arrow_forwardIn Exercises 14 and 15, use a graphing utility to graph the function. If the function is periodic, find its period. If not, describe the behavior of the function as x increases without bound. y=6xcos0.25xarrow_forwardIn Exercises 14 and 15, use a graphing utility to graph the function. If the function is periodic, find its period. If not, describe the behavior of the function as x increases without bound. y=sin2x+2cosxarrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning