Finding and Analyzing Derivatives Using Technology In Exercises 49-54, (a) use a computer algebra system to differentiate the function, (b) sketch the graphs of f and f ' on the same set of coordinate axes over the given interval, (c) find the critical numbers of f in the open interval, and (d) find the interval(s) on which f ' is positive and the interval(s) on which f ' is negative. Compare the behavior of f and the sign of f ' . f ( x ) = 10 ( 5 − x 2 − 3 x + 16 ) , [ 0 , 5 ]
Finding and Analyzing Derivatives Using Technology In Exercises 49-54, (a) use a computer algebra system to differentiate the function, (b) sketch the graphs of f and f ' on the same set of coordinate axes over the given interval, (c) find the critical numbers of f in the open interval, and (d) find the interval(s) on which f ' is positive and the interval(s) on which f ' is negative. Compare the behavior of f and the sign of f ' . f ( x ) = 10 ( 5 − x 2 − 3 x + 16 ) , [ 0 , 5 ]
Solution Summary: The author explains how the Ti-83 calculator can be sued to plot the graph of both the functions.
Finding and Analyzing Derivatives Using Technology In Exercises 49-54, (a) use a computer algebra system to differentiate the function, (b) sketch the graphs of f and
f
'
on the same set of coordinate axes over the given interval, (c) find the critical numbers of f in the open interval, and (d) find the interval(s) on which
f
'
is positive and the interval(s) on which
f
'
is negative. Compare the behavior of f and the sign of
f
'
.
1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
=
5 37
A 4 8 0.5
06
9
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY