Concept explainers
Finding an Equation of a Tangent Line In Exercises 47-54, find an equation of the tangent line to the graph of the function at the given point. Then use a graphing utility to graph the function and the tangent line in the same viewing window. See Example 5.
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Calculus: An Applied Approach (MindTap Course List)
- The radii of the pedal sprocket, the wheel sprocket, and the wheel of the bicycle in the figure are 4 inches, 2 inches, and 14 inches, respectively. A cyclist is pedaling at a rate of 1 revolution per second. (a) Find the speed of the bicycle in feet per second and miles per hour. (b) Use your result from part (a) to write a function for the distance d (in miles) a cyclist travels in terms of the number n of revolutions of the pedal sprocket. (c) Write a function for the distance d (in miles) a cyclist travels in terms of time t (in seconds). Compare this function with the function from part (b).arrow_forwardThink About It Does adding a constant term to a function affect the existence of an inverse function? Explain.arrow_forwardA Ferris wheel has a radius of 35 feet. The bottom of the Ferris wheel sits 0.7 feet above the ground. You board the Ferris wheel at the 6 o'clock position and rotate counter-clockwise. a. Write a function f that determines your height above the ground (in feet) in terms of the number of radians you have swept out from the 6 o'clock position, a. f(a) = tan(35) Preview b. Write a function g, that determines your height above the ground (in feet) in terms of the number of feet you have traveled since you started rotating, s. g(s) : Previewarrow_forward
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- Business calc question Find the derivative of the functionarrow_forwardTemperature The graph shows the temperature in degrees Celsius as a function of the altitude h in feet when an inversion layer is over Southern California. See Exercise 43 in the previous section. Estimate and interpret the derivatives of T(h) at the marked points.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,