Finding an Equation of a Tangent Line In Exercises 45-50, (a) find an 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. See Example 10.
Trending nowThis is a popular solution!
Chapter 2 Solutions
Bundle: Calculus: An Applied Approach, Loose-Leaf Version, 10th + WebAssign Printed Access Card for Larson's Calculus: An Applied Approach, 10th Edition, Single-Term
- Anthropologists can estimate a person's height from the length of certain bones. The height h (in inches) of an adult human female can be modeled by the function h(1) where / is the length (in inches) of the femur, or thigh bone. (a) Find the domain and range of the function. (Round your answers to 2 decimal places.) Domain: ? ↑ ? ↑ Range: ? ↑ (b) Suppose a female's femur was 16 inches long. About how tall was she? (Round your answers to the nearest inch.) ft in Need Help? ? (c) If an anthropologist estimates a female's height to be 5 feet 3 inches, about how long was her femur? (Round your answer to 2 decimal places.) in Read It ↑ Talk to a Tutor = 1.94/+ 28.4, 16 ≤ / ≤ 25,arrow_forwardConsider the function f(x) = (1/2)². (a) Complete the table of values of f(x) for x=-3, -2,-1,0,1, 2, 3. -3 I f(x) (b) Which of the graphs below could represent the graph of f(x)?? -2 A B D 0 HIIN E F 2arrow_forwardIn Exercises 43 and 44, graph the functions. Notice in each case that the numerator and denominator contain at least one com- mon factor. Thus you can simplify each quotient; but don't lose track of the domain of the function as it was initially defined. x + 2 x² - 4 43. (a) y (b) y = (c) y = X + 2 X-2 X-1 (x - 1)(x-2)arrow_forward
- F(x)=(x-1)^2-2 Sketch the graph of each function.use the axis of symmetry ,Y intercept ,X intercepts or a table of values Also show the work thank youarrow_forwardCalculus question attached.arrow_forwardThe graph of a function f with domain [-3,3] is shown in the figure. Sketch the graph of y = f -1(x).arrow_forward
- Pls help ASAP. Pls show all work.arrow_forwardUnder a microscope, Ms. Kapinski studies a culture with bacteria. As the number of hours progresses, Ms. Kapinski sees that the bacteria can be modeled by the function ?(?) = 1290(0.76) ? where b represents the number of bacteria t hours after Ms. Kapinski begins her study. (a) What does the value 0.76 represent in this situation? Be sure to explain. (b) What does the value 1290 represent in this situation? Be sure to explain. (c) The number of bacteria in a second study is modeled by the function ?2 (?) = 1180(1.76) ? . i. What does the value of 1180 represent in this situation? ii. What does the difference of 1290 and 1180 mean between the two studies? iii. What does the difference between 0.76 and 1.76 mean between the two studies?arrow_forwardPart D: Algebraic Manipulation Practice Use the limit definition of the derivative to find the derivative of the function 3x – 7 f(x) V5x2 + 1arrow_forward
- Identify the domain and range of the function, and then sketch the graph of the function without using a graphing utility. (a) f(x) = 1+In(x-2) (b) g(x) = 3+ e"-2 %3Darrow_forwardPlot the Function x+earrow_forwardBody surface area is an important piece of medical information because it is a factor in temperature regulation as well as some drug level determinations. The Mosteller formulat gives one way of estimating body surface area 8 in square meters. The formula uses the weight w in kilograms and the height h in centimeters. The relation is Vhw 60 In this exercise we consider people who are 190 centimeters tall. (a) Write a formula for 8 as a function of w. (b) Make a graph of 8 versus w. Include weights up to 100 kilograms. 3.0 3.0r 25 25 20 20 15 15 1.0 1.0 05 0.5 00 w 00 20 40 60 80 100 20 40 60 80 100 3.0. 3.0 25 25 20 20 1.5 15 1.0 1.0 05 05 w 100 0.0 20 10 60 80 20 10 60 80 100 (c) Is the graph you made in part (b) concave up or concave down? O concave up O concave down (d) In this part we consider the effect of weight gain on men who are 190 centimeters tall. Would the weight gain have a greater effect on surface area for a lighter man or for a he avier man? O lighter man O heavier manarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage