Finding the Slope of a Graph In Exercises 37-44, find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. See Examples 3 and 9.
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- LIFE SCIENCE APPLICATIONS APPLY IT Splenic Artery Resistance Blood flow to the fetal spleen is of research interest because several diseases are associated with increased resistance in the splenic artery the artery that goes to the spleen. Researchers have found that the index of splenic artery resistance in the fetus can be described by the function y=0.057x0.001x2, where x is the number of weeks of gestation. Source: American Journal of Obstetrics and Gynecology. a. At how many weeks is the splenic artery resistance a maximum? b. What is the maximum splenic artery resistance? c. At how many weeks is the splenic artery resistance equal to 0, according to this formula? Is your answer reasonable for this function? Explain.arrow_forwardHow do you find the value of a function?arrow_forwardAnalyze and sketch the graph of the function. f(x) = xe−xarrow_forward
- Write a relationship for a function whose f(x) values are 3 more than the principal square root of xarrow_forwardMake a sign diagram for the derivative of the function. f(x) = −x4 + 8x3 − 16x2 + 3 x= x= Find all open intervals of increase and decrease. (Enter your answers using interval notation.) Increase Decrease Sketch the graph of the function.arrow_forwardThe graph to the right was created by vertically shifting the graph of the basic function y=-. Write a function that describes the graph to the right. X The function that describes the graph is f(x) =. (Simplify your answer.) f(x)arrow_forward
- 2. Summarize what you have learned about functions. Can all relationships between variables qualify as functions? How can you represent and describe functions? How are functions useful in the real world?arrow_forwardA right triangle is formed in the first quadrant by the x- and y-axes and a line through the point (2, 1) see figure. Write the area A of the triangle as a function of x, and determine the domain of the function.arrow_forwardApplication - Forestry A team of researchers finds that there is a relationship between the overall health of a forest they're studying and the population of a certain beetle which feeds on the bark of old-growth trees. Due to the warming climate, the beetles are now able to reproduce one more time per year than they previously did, exacerbating the stress caused by the drought 13x³ +67 of the past few seasons. They use the function f(x) to model the relationship between the two populations, .6x5 +39 where x is in tens of thousands of beetles and f is in thousands of trees. They note that there is a beneficial contribution to the ecosystem as a whole for a smaller population of the beetles, but that the number of healthy trees sharply declines as the beetle population rises too much. - 1. Graph f(x) using technology. a. What appears to be the maximum number of healthy trees, to the nearest thousand? What is the estimated beetle population corresponding to this, to the nearest ten…arrow_forward
- The figure shows the cost of mailing a first-class letter, f(x), in a country as a function of its weight, x, in ounces. What is the cost of mailing a letter that weighs 1.7 ounces? 1.41- 1.19- 0.97- 0.75- 0.53- 0.31 0123 456 Weight (ounces) The cost is $ Cost (dollars)arrow_forwardDifferientiate the function. y=(2x-5)3(3-x4)4arrow_forwardPersonal Expenditures Personal consumption expenditures for durable goods in the United States, inbillions of dollars, can be modeled by the functionP(x) = 306.472x0.464, where x is the number ofyears after 1990. Rewrite the function with x equal tothe number of years after 1995. (Hint: Shift the x-valueby the difference in years.)arrow_forward
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,