A. Consider the function/(x)=-3x²+2x. Find the average rate of change from x-1 tox-3. Using your calculator, explore (as directed below) to find the instantaneous rate of change at x-2. Remember, this will be the slope of the tangent line. Follow the instructions below. The first function (y) is the function under consideration. The next five (yz through ye) you are going to explore to find which one is the tangent line. Note: A tangent line will touch the curve at only one point in the immediate area you are observing. Since you are zoomed in rather closely, however, it will look like every line is touching the curve at only one point. Note that the real tangent line will not "cross through the curve at the given point, it will only "touch" the curve. Another way to think of it is that the tangent line will not cross from one side of the curve to the other, but remain on one side where it skirts the edge in one point and keeps going. Given the limits of the calculator and the inability to zoom in sufficiently, it may appear that the tangent line hits in multiple spots. However, knowing that one of the lines y through ye actually is the tangent line, you should be able to pick the correct one as you change windows and zoom in. First type in the functions. Then set the WINDOW 1 values given below. Graph and observe. Then set a new window using the WINDOW 2 values below. Graph and observe. Set a 3 window using the WINDOW 3 values below. Graph and observe. Type in your calculator in the function screen: 3₁ =-3x² + 2x y/₂ = -5x+2 y₁ =-6x+4 J', = -8x+8 y=-10x+12 y = -13x+18 Start with the 1" window, then zoom with the 2, then the 3: WINDOW 1 WINDOW 2 WINDOW3 Xmin | Xmin Xmin J Xmax 5 Xmax-4 Xsel 1 Xsel 1 Ymin -10 Ymin10 Ymax 5 Ymax A Ysel - I Ysel-1 Which of the lines ya through ye is the tangent line to the curve yi atx=2? Write it in the box and circle it above. Examine the equation of that line. What is the slope of the line? Xmax-3 Xsel-1 Ymin=-16 Ymax Yscl-1 2. 3.
A. Consider the function/(x)=-3x²+2x. Find the average rate of change from x-1 tox-3. Using your calculator, explore (as directed below) to find the instantaneous rate of change at x-2. Remember, this will be the slope of the tangent line. Follow the instructions below. The first function (y) is the function under consideration. The next five (yz through ye) you are going to explore to find which one is the tangent line. Note: A tangent line will touch the curve at only one point in the immediate area you are observing. Since you are zoomed in rather closely, however, it will look like every line is touching the curve at only one point. Note that the real tangent line will not "cross through the curve at the given point, it will only "touch" the curve. Another way to think of it is that the tangent line will not cross from one side of the curve to the other, but remain on one side where it skirts the edge in one point and keeps going. Given the limits of the calculator and the inability to zoom in sufficiently, it may appear that the tangent line hits in multiple spots. However, knowing that one of the lines y through ye actually is the tangent line, you should be able to pick the correct one as you change windows and zoom in. First type in the functions. Then set the WINDOW 1 values given below. Graph and observe. Then set a new window using the WINDOW 2 values below. Graph and observe. Set a 3 window using the WINDOW 3 values below. Graph and observe. Type in your calculator in the function screen: 3₁ =-3x² + 2x y/₂ = -5x+2 y₁ =-6x+4 J', = -8x+8 y=-10x+12 y = -13x+18 Start with the 1" window, then zoom with the 2, then the 3: WINDOW 1 WINDOW 2 WINDOW3 Xmin | Xmin Xmin J Xmax 5 Xmax-4 Xsel 1 Xsel 1 Ymin -10 Ymin10 Ymax 5 Ymax A Ysel - I Ysel-1 Which of the lines ya through ye is the tangent line to the curve yi atx=2? Write it in the box and circle it above. Examine the equation of that line. What is the slope of the line? Xmax-3 Xsel-1 Ymin=-16 Ymax Yscl-1 2. 3.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:A. Consider the function/(x)=-3x²+2x.
Find the average rate of change from x-1 tox-3.
Using your calculator, explore (as directed below) to find the instantaneous rate of change at x-2.
Remember, this will be the slope of the tangent line.
na and prOVIN
Follow the instructions below. The first function (ys) is the function under consideration.
The next five (ya through ye) you are going to explore to find which one is the tangent line.
Note: A tangent line will touch the curve at only one point in the immediate area you are
observing. Since you are zoomed in rather closely, however, it will look like every line is touching
the curve at only one point.
Note that the real tangent line will not "cross" through the curve at the given point, it will only.
"touch" the curve. Another way to think of it is that the tangent line will not cross from one side of
the curve to the other, but remain on one side where it skirts the edge in one point and keeps
going. Given the limits of the calculator and the inability to zoom in sufficiently, it may appear that
the tangent line hits in multiple spots. However, knowing that one of the lines ya through yo
actually is the tangent line, you should be able to pick the correct one as you change windows
and zoom in.
First type in the functions. Then set the WINDOW 1 values given below. Graph and observe.
Then set a new window using the WINDOW 2 values below. Graph and observe.
Set a 3d window using the WINDOW 3 values below. Graph and observe.
Type in your calculator
in the function screen:
2x
3 =-3x² +
J. ~Sr|2
|y₁ = -6x +4
3₁ = -8x+8
=-10x+12
y=-13x+18-
Start with the 1" window, then zoom with the 2, then the 3:
WINDOW 1
WINDOW 2
WINDOW3
Xmin
Xmin -4
Amin -
Xmax 5
Xmax-4
Xmax 3.
Xsel 1
Xsel-1
Xsel 1
Ymin -10
Ymin = 20
Ymin=16
Ymax 5
Ymax
Ysel 1
Ysel-1
Which of the lines ya through yo is the tangent line to the curve y₁ at x = 2?
Write it in the box and circle it above.
Examine the equation of that line. What is the slope of the line?
Ymax |
Yscl-1
2.
3.
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