Finding an Equation of a Tangent Line In exercises 67-74, (a) find in equation of the tangent line to the graph of the function at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results.
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Chapter 5 Solutions
EBK CALCULUS: EARLY TRANSCENDENTAL FUNC
- (Differentiable Functions: Standard Analysis & Graph Sketching). Consider the function f(x) = −(2x+11x+16)/e^x(i) Make the standard analysis of the function f(x), that is: (1) make the combined sign chart of f' and f''; (ii) Use (i) to sketch the graph of f ;arrow_forwardConsider the function y = (a) Find a formula for the slope of the tangent line to the graph of f at a general point x = xo. Mtan = Use the formula obtained in part (a) to find the slope of the tangent line for the given value of xo. (b) mtan 756 f(x) = x² + 15x + 56 and the x-value xo 5. = =arrow_forwardEquation of a tangent line Let f(x) = -16x 2 + 96x (the position function examined in Section 2.1) and consider the point P(1, 80) on the curve. a. Find the slope of the line tangent to the graph of f at P. b. Find an equation of the tangent line in part (a).arrow_forward
- topic: Elimination of arbitrary constants by differentiation and combinationarrow_forwardAlgebraically determine the x- and y-intercepts of y = ln(x +2)arrow_forwardFind an equation of the tangent line to the graph of f at the given point, (a) use a graphing utility to graph the function and its tangent line at the point, and (b) use the tangent feature of a graphing utility to confirm your results. f(x) = x + 4/x , (−4, −5)arrow_forward
- Finding a Derivative In Exercises 17–42, findthe derivative of the function. \text { 17. } f(x)=\arcsin (x-1)arrow_forwardFind an equation of the tangent line to the graph of f at the given point, (a) use a graphing utility to graph the function and its tangent line at the point, and (b) use the tangent feature of a graphing utility to confirm your results f(x) = (x3 + 4x − 1)(x − 2), (1, −4)arrow_forwardFinding an Equation of a Tangent Line In Exercises43–46, find an equation of the tangent line to the graph of f atthe given point.43. f (x) = (x + 2)(x2 + 5), (−1, 6)arrow_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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