
Modeling Data The average typing speeds S (in words per minute) of a typing student after t weeks of lessons are shown in the table.
t |
5 |
10 |
15 |
20 |
25 |
30 |
S |
28 |
56 |
79 |
90 |
93 |
94 |
A model for the data is
(a) Use a graphing utility to plot the data and graph the model.
(b) Use the second derivative to determine the concavity of S. Compare the result with the graph in part (a).
(c) What is the sign of the first derivative for t > 0? By combining this information with the concavity of the model, what inferences can be made about the typing speed as t increases?

Trending nowThis is a popular solution!

Chapter 3 Solutions
Calculus
- 8. For x>_1, the continuous function g is decreasing and positive. A portion of the graph of g is shown above. For n>_1, the nth term of the series summation from n=1 to infinity a_n is defined by a_n=g(n). If intergral 1 to infinity g(x)dx converges to 8, which of the following could be true? A) summation n=1 to infinity a_n = 6. B) summation n=1 to infinity a_n =8. C) summation n=1 to infinity a_n = 10. D) summation n=1 to infinity a_n diverges.arrow_forwardPLEASE SHOW ME THE RIGHT ANSWER/SOLUTION SHOW ME ALL THE NEDDED STEP 13: If the perimeter of a square is shrinking at a rate of 8 inches per second, find the rate at which its area is changing when its area is 25 square inches.arrow_forwardDO NOT GIVE THE WRONG ANSWER SHOW ME ALL THE NEEDED STEPS 11: A rectangle has a base that is growing at a rate of 3 inches per second and a height that is shrinking at a rate of one inch per second. When the base is 12 inches and the height is 5 inches, at what rate is the area of the rectangle changing?arrow_forward
- please answer by showing all the dfalowing necessary step DO NOT GIVE ME THE WRONG ANSWER The sides of a cube of ice are melting at a rate of 1 inch per hour. When its volume is 64 cubic inches, at what rate is its volume changing?arrow_forwardSox & Sin (px) dx 0arrow_forward8 L 8 e ipx dxarrow_forward
- Find the Taylor polynomial T³(×) for the function f centered at the number a. f(x) = xe-2x a = 0 T3(x) =arrow_forwardFor each graph in Figure 16, determine whether f (1) is larger or smaller than the slope of the secant line between x = 1 and x = 1 + h for h > 0. Explain your reasoningarrow_forwardPoints z1 and z2 are shown on the graph.z1 is at (4 real,6 imaginary), z2 is at (-5 real, 2 imaginary)Part A: Identify the points in standard form and find the distance between them.Part B: Give the complex conjugate of z2 and explain how to find it geometrically.Part C: Find z2 − z1 geometrically and explain your steps.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning




