54. Use the function f in the figure below and the function g defined by g(x) = | f(t) dt. 0 |1|2| 3| 4 | 5 | 6 | 7 | 8 | 9 | 10 g(x) a) Complete the table. b) Plot the points from the table in part (a). c) Where does g have its minimum? Explain. d) Which four consecutive points are collinear? Explain. e) Between which two consecutive points does g increase at the greatest rate? Explain. 1 1 3 4 7 8. 10 -1
54. Use the function f in the figure below and the function g defined by g(x) = | f(t) dt. 0 |1|2| 3| 4 | 5 | 6 | 7 | 8 | 9 | 10 g(x) a) Complete the table. b) Plot the points from the table in part (a). c) Where does g have its minimum? Explain. d) Which four consecutive points are collinear? Explain. e) Between which two consecutive points does g increase at the greatest rate? Explain. 1 1 3 4 7 8. 10 -1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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the function is g(x)=
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Step 1
Here we can note that the function g(x) denote the net area under f(x) from 0 to x as its formula is
Hence to find g(x) at x=a, we just need to find the net area under f(x) from 0 to a.
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