The graph in Exercise 64 shows the number of student y enrolled in public colleges for selected years x , where x is the number of years since 1990. The table gives a partial list of data from the graph. a. Use the data in the table to find the least-squares regression line. Round the slope to 2 decimal places and the y -intercept to 1 decimal place. b. Use a graphing utility to graph the regression line and the observed data. c. Assuming that the linear trend continues use the model from part (a) to predict the number of students enrolled in public colleges for the year 2020. d. By how much do the results of part (c) differ from the result of Exercise 64(d)?
The graph in Exercise 64 shows the number of student y enrolled in public colleges for selected years x , where x is the number of years since 1990. The table gives a partial list of data from the graph. a. Use the data in the table to find the least-squares regression line. Round the slope to 2 decimal places and the y -intercept to 1 decimal place. b. Use a graphing utility to graph the regression line and the observed data. c. Assuming that the linear trend continues use the model from part (a) to predict the number of students enrolled in public colleges for the year 2020. d. By how much do the results of part (c) differ from the result of Exercise 64(d)?
Solution Summary: The author calculates the least squares regression line by rounding the slope to 2 decimal and y-intercept.
The graph in Exercise 64 shows the number of student y enrolled in public colleges for selected years x, where x is the number of years since 1990. The table gives a partial list of data from the graph.
a. Use the data in the table to find the least-squares regression line. Round the slope to 2 decimal places and the y-intercept to 1 decimal place.
b. Use a graphing utility to graph the regression line and the observed data.
c. Assuming that the linear trend continues use the model from part (a) to predict the number of students enrolled in public colleges for the year 2020.
d. By how much do the results of part (c) differ from the result of Exercise 64(d)?
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
University Calculus: Early Transcendentals (4th Edition)
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