For Exercises 69–84, draw a graph to match the description given. Answers will vary.
has a negative derivative over
and
and a positive derivative over
and
but
does not exist.
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Chapter 2 Solutions
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Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Calculus: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals (4th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Glencoe Math Accelerated, Student Edition
- In Exercises 59–61: a. Find the local extrema of each function on the given interval, and say where they occur. b. Graph the function and its derivative together. Comment on the behavior of ƒ in relation to the signs and values of ƒ′. 59. ƒ(x) = sin 2x, 0 <=x<= pai 60. ƒ(x) = sin x - cos x, 0<= x<=2pai 61. ƒ(x) = sqrt(3 cos x) + sin x, 0<= x<= 2paiarrow_forwardIn Exercises 93–96, use the table of values to calculate the derivative of the function at the given point. 1 4 6. f(x) f'(x) g(x) g'(x) 4 6. 7 4 4 1 1 5 } 3arrow_forwardIn Exercises 13–16, differentiate the functions and find the slope of the tangent line at the given value of the independent variable. 13. ƒ(x) = x +9/x ,x=-3 14. k(x) = 1/( 2 + x),x=2 15. s = t3 - t2, t = -1 16. (x + 3)/( 1 - x) , x = -2arrow_forward
- Find the linearization of the function f(x) = 1/(9x+8) at x = -1.arrow_forwardFind the linearization at ?=a ?(?)=2x3 a=1arrow_forwardUse the definition of the derivative to find the equations of the lines described in Exercises 59–64. 59. The tangent line to f(x) = x² at x = -3. 60. The tangent line to f(x) = x² at x = 0. 61. The line tangent to the graph of y = 1 – x – x² at the point (1, –1). 62. The line tangent to the graph of y = 4x + 3 at the point (-2, –5). %3D 63. The line that passes through the point (3, 2) and is parallel to the tangent line to f(x) = - at x = -1. 64. The line that is perpendicular to the tangent line to f (x) = x4 +1 at x = 2 and also passes through the point (–1, 8). For each function f graphed in Exercises 65–68, determine the values of x at which f fails to be continuous and/or differen- tiable. At such points, determine any left or right continuity or differentiability. Sketch secant lines supporting your answers.arrow_forward
- Suppose f is a linear function such that f(3) = 6 and f(7) = 1. Find the equation for f with respect to x. (Express to 2 decimal places, if needed.) f(x) =arrow_forwardThe point Q (-4,7) lies on the function f(x). Suppose f(x) is transformed according to: y=-3 f [0.5(x + 3)] + 5. Determine the x-coordinate of the transformed point, Q'. Enter only the x-coordinate, a single value, rounded correctly to 2 decimal places (ie 3.46 or 7.00 or 1.50)arrow_forwardFind the linearization of the function at x = a = -4arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning
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