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
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the function is g(x)=integral from 0 to x f(t)dt

954. Use the function ƒ in the figure below and the function g defined by g(x) = | f(t) dt.
0| 12 |3 4 5 6 78 | 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.
f
1
1
3
8
9.
10
-1
Transcribed Image Text:954. Use the function ƒ in the figure below and the function g defined by g(x) = | f(t) dt. 0| 12 |3 4 5 6 78 | 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. f 1 1 3 8 9. 10 -1
Expert Solution
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 

g(x)=0xf(t) dt

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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