CALCULUS:GRAPHICAL,NUMERICAL,..-PACKAGE
5th Edition
ISBN: 9780133320381
Author: Finney
Publisher: SAVVAS L
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4
er Session 1 20.
Solve the problem.
The slope to the tangent line of a curve is given by f(x) = x2 - 9x + 12. If the point (0, 9) is on the curve, find an equation of
the curve.
Select one:
А.
" f(x) =- 10x2 + 12x + 9
9.
B. f) =Dx-글x+ 12x + 9
C. f) =-+ 12x +1
%3D
D. f(x) =x - 10x2 + 12x + 1
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What is the slope of the tangent line to the function:
f (x) = In (2 x² + 2 x – 11)
at the point P(2,0)?
m =
Find the equation of the tangent line to the point P(2,0).The answer should be written in slope-intercept form.
y =
symbolic formatting help
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- bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.arrow_forwardLater High School Graduates This is a continuation of Exercise 16. The following table shows the number, in millions, graduating from high school in the United States in the given year. Year Number graduating in millions 2001 2.85 2003 2.98 2005 3.11 2007 3.24 a. Find the slope of the linear function modeling high school graduations, and explain in practical terms the meaning of the slope. b. Find a formula for a linear function that models these data. c. Express, using functional notation, the number graduating from high school in 2008, and then calculate the value. d. The actual number graduating from high school in 1994 was about 2.52 million. Compare this with the value given by the formula in part b and with your answer to part of Exercise 16. Which is closer to the actual value? In general terms, what was the trend in high school graduations from 1985 to 2007? 16. High School Graduates The following table shows the number, in millions, graduating from high school in the United States in the given year.16 Year Number graduating in millions 1985 2.83 1987 2.65 1989 2.47 1991 2.29 a. By calculating difference, show that these data can be modeled using a linear function. b. What is the slope for the linear function modeling high school graduations? Explain in practical terms the meaning of the slope. c. Find a formula for a linear function that models these data. d. Express, using functional notation, the number graduating from high school in 1994, and then use your formula from part c to calculate that value.arrow_forwardLinearize the function f(x) = a3 + 2x + 4 at a = 3.arrow_forward
- The linear function f(x) = 48.8x + 63.8 models the number of smartphones sold in some country, f(x), in millions, x years after 2006. Find the slope of the model. Then describe what this means in terms of the rate of change of the dependent variable per unit change in the independent variable. The slope of the model is . (Type an integer or a decimal.)arrow_forwardFind equations of the tangent line and the normal line to the graph of the function f(x) = 5x² + 8 at the point (-3,53). %3D (Express numbers in exact form. Use symbolic notation and fractions where needed. Let y = f(x) and give the equations in %3D terms of y and x.) tangent line equation: normal line equation: Select the image containing the graph of the function, the tangent line, and the normal line at the indicated point on the same set of coordinate axes.arrow_forwardInstead of using the tangent line to estimate the value of the functions, we could estimate when the function attains certain values. Consider the function f(x) =x - 7. The graph is now zoomed in to better show the tangent line at the point (3, f(3)). Using your tangent line from the previous slide, determine where the linearization attains the value of -8. Show your work in the text box below,. Compare the x value where the linearization attained a value of zero and where the function f(x) = -8. How do these two values compare?arrow_forward
- By using r -software please for parts f and garrow_forward- Semester 1 A A poll commissioned by a politician estimates that t days after he makes a statement denegrating women, the percentage of his constituency (those who support him at the time he made the statement) that still supports him is given by S(t) 75(t? – 3t + 25) t2 + 3t + 25 The election is 10 days after he made the statement. (i) If the derivative S'(t) may be thought of as an approval rate, derivate the a function for his approval rate. (ii) When was his support at its lowest level? (iii) What was his minimum support level? (iv) Was the approval rate positive or negative on the date of the election? (c) Lara offers 100 autograph bats. If each is priced at p dollars, it is that the demand curve dq dp If price elasticily is E(p) 4 %3D for the p 1l be p = 250 %3D 1 demand is elastic.arrow_forward
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