Find the equation of the Tangent Line and Normal Line of the given equation at the given point. Graph the function and lines ▪ f(x)=2x²-3x²-2x+5 Script 1% This program computes for the Tangent Line / Normal Line of a curve % about a given point 2 %define x for symbolic processing 3 4 %IDENTIFY the function f(x) 5 f(x) = 6 7 %DETERMINE the point of tangency (This will be a random point) 8 x0=randi ([-5,5]) 9 %SOLVE for the ordinate of the point of tangency 10 yo=f(x0); %Evaluate y given value fox 11 12 %FIND the slope function 13 yprime = 14 %Determine the slope at the given xo %Evaluate the slope 16 m 17 18 %Solve the equation of the tangent line 19 ytangent= 20 21 %Solve the Equation of the normal line 22 ynormal = 23 %Solve for the first derivative ✓ 24 %DISPLAYING RESULTS 25 fprintf('The tangent line to f(x) =%s at (%.2f, %.2f) is y = %s\n', string(f(x)),x0,ye, string(ytangent)) 26 fprintf('The normal line to f(x) =%s at (%.2f, %.2f) is y = %s \n',string(f(x)), x0, yo, string(ynormal)) 27 28 %PLOTTING 20 21 % Solve the Equation of the normal line 22 ynormal = 23 28 %PLOTTING 29 g1-ezplot (f, [-15, 15]); 30 set (g1, 'color', 'b') 31 grid on 32 hold on 24 %DISPLAYING RESULTS 25 fprintf('The tangent line to f(x) =%s at (%.2f, %.2f) is y = %s\n', string(f(x)),x0,ye, string(ytangent)) 26 fprintf('The normal line to f(x) =%s at (%.2f , %.2f) is y = %s \n', string(f(x)),x0,ye, string(ynormal)) 27 33 plot (x0, ye, '*') 34 text (x0+1, yo, "Point of Tangency") 35 g2=ezplot(ytangent, [-15,15]); 36 text (5,5, ["y (Tangent)=", string(ytangent)]) 37 pause (1) 38 set (g2, 'color', 'm') 39 pause (1) Save 40 g3=ezplot(ynormal, [-15,15]); 41 text(3,3, ["y (Normal)=", string(ynormal)]) 42 set (g3, 'color', 'c'); 43 title("Tangent Line and Normal Line") 44 C Reset MATLAB Documentat
Find the equation of the Tangent Line and Normal Line of the given equation at the given point. Graph the function and lines ▪ f(x)=2x²-3x²-2x+5 Script 1% This program computes for the Tangent Line / Normal Line of a curve % about a given point 2 %define x for symbolic processing 3 4 %IDENTIFY the function f(x) 5 f(x) = 6 7 %DETERMINE the point of tangency (This will be a random point) 8 x0=randi ([-5,5]) 9 %SOLVE for the ordinate of the point of tangency 10 yo=f(x0); %Evaluate y given value fox 11 12 %FIND the slope function 13 yprime = 14 %Determine the slope at the given xo %Evaluate the slope 16 m 17 18 %Solve the equation of the tangent line 19 ytangent= 20 21 %Solve the Equation of the normal line 22 ynormal = 23 %Solve for the first derivative ✓ 24 %DISPLAYING RESULTS 25 fprintf('The tangent line to f(x) =%s at (%.2f, %.2f) is y = %s\n', string(f(x)),x0,ye, string(ytangent)) 26 fprintf('The normal line to f(x) =%s at (%.2f, %.2f) is y = %s \n',string(f(x)), x0, yo, string(ynormal)) 27 28 %PLOTTING 20 21 % Solve the Equation of the normal line 22 ynormal = 23 28 %PLOTTING 29 g1-ezplot (f, [-15, 15]); 30 set (g1, 'color', 'b') 31 grid on 32 hold on 24 %DISPLAYING RESULTS 25 fprintf('The tangent line to f(x) =%s at (%.2f, %.2f) is y = %s\n', string(f(x)),x0,ye, string(ytangent)) 26 fprintf('The normal line to f(x) =%s at (%.2f , %.2f) is y = %s \n', string(f(x)),x0,ye, string(ynormal)) 27 33 plot (x0, ye, '*') 34 text (x0+1, yo, "Point of Tangency") 35 g2=ezplot(ytangent, [-15,15]); 36 text (5,5, ["y (Tangent)=", string(ytangent)]) 37 pause (1) 38 set (g2, 'color', 'm') 39 pause (1) Save 40 g3=ezplot(ynormal, [-15,15]); 41 text(3,3, ["y (Normal)=", string(ynormal)]) 42 set (g3, 'color', 'c'); 43 title("Tangent Line and Normal Line") 44 C Reset MATLAB Documentat
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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Question
DO THIS IN MATLAB
![Activity:
Find the equation of the Tangent Line and Normal Line of the given equation at the given point. Graph the function and lines
▪ f(x) = 2x²-3x² - 2x+5
Script>
1% This program computes for the Tangent Line / Normal Line of a curve % about a given point
2
%define x for symbolic processing
3
4 %IDENTIFY the function f(x)
5 f(x) =
6
7 %DETERMINE the point of tangency (This will be a random point)
8 x0=randi ([-5,5])
9 %SOLVE for the Ordinate of the point of tangency
10 y0=f(x0); %Evaluate y given value fo x
11
12 %FIND the slope function
13 yprime =
14
15 %Determine the slope at the given x0
16 m=
%Evaluate the slope
17
18 %Solve the equation of the tangent line
19 ytangent=
20
21 %Solve the Equation of the normal line
22 ynormal =
23
%Solve for the first derivative
24 %DISPLAYING RESULTS
25 fprintf('The tangent line to f(x)=%s at (%.2f, %.2f) is y = %s\n', string(f(x)),x0,yo, string(ytangent))
26 fprintf('The normal line to f(x) = %s at (%.2f, %.2f) is y = %s\n',string(f(x)),x0,yo, string(ynormal))
27
28 %PLOTTING
20
21 %Solve the Equation of the normal line
22 ynormal =
23
Save
24 %DISPLAYING RESULTS
25 fprintf('The tangent line to f(x)=%s at (%.2f, %.2f) is y = %s\n', string(f(x)),x0,yo, string(ytangent))
26 fprintf('The normal line to f(x)=%s at (%.2f, %.2f) is y = %s\n',string(f(x)), x0, yo, string(ynormal))
27
28 %PLOTTING
29 g1-ezplot (f, [-15,15]);
30 set (g1, 'color', 'b')
31 grid on
32 hold on
33 plot (x0, yo,'*')
34 text (x0+1, yo, "Point of Tangency")
35 g2-ezplot(ytangent, [-15,15]);
36 text (5,5, ["y (Tangent)=", string(ytangent)])
37 pause (1)
38 set (g2, 'color', 'm')
39 pause (1)
40 g3=ezplot(ynormal, [-15,15]);
41 text (3,3, ["y (Normal)=", string(ynormal)])
42 set (g3, 'color', 'c');
43 title("Tangent Line and Normal Line")
44
C Reset
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Transcribed Image Text:Activity:
Find the equation of the Tangent Line and Normal Line of the given equation at the given point. Graph the function and lines
▪ f(x) = 2x²-3x² - 2x+5
Script>
1% This program computes for the Tangent Line / Normal Line of a curve % about a given point
2
%define x for symbolic processing
3
4 %IDENTIFY the function f(x)
5 f(x) =
6
7 %DETERMINE the point of tangency (This will be a random point)
8 x0=randi ([-5,5])
9 %SOLVE for the Ordinate of the point of tangency
10 y0=f(x0); %Evaluate y given value fo x
11
12 %FIND the slope function
13 yprime =
14
15 %Determine the slope at the given x0
16 m=
%Evaluate the slope
17
18 %Solve the equation of the tangent line
19 ytangent=
20
21 %Solve the Equation of the normal line
22 ynormal =
23
%Solve for the first derivative
24 %DISPLAYING RESULTS
25 fprintf('The tangent line to f(x)=%s at (%.2f, %.2f) is y = %s\n', string(f(x)),x0,yo, string(ytangent))
26 fprintf('The normal line to f(x) = %s at (%.2f, %.2f) is y = %s\n',string(f(x)),x0,yo, string(ynormal))
27
28 %PLOTTING
20
21 %Solve the Equation of the normal line
22 ynormal =
23
Save
24 %DISPLAYING RESULTS
25 fprintf('The tangent line to f(x)=%s at (%.2f, %.2f) is y = %s\n', string(f(x)),x0,yo, string(ytangent))
26 fprintf('The normal line to f(x)=%s at (%.2f, %.2f) is y = %s\n',string(f(x)), x0, yo, string(ynormal))
27
28 %PLOTTING
29 g1-ezplot (f, [-15,15]);
30 set (g1, 'color', 'b')
31 grid on
32 hold on
33 plot (x0, yo,'*')
34 text (x0+1, yo, "Point of Tangency")
35 g2-ezplot(ytangent, [-15,15]);
36 text (5,5, ["y (Tangent)=", string(ytangent)])
37 pause (1)
38 set (g2, 'color', 'm')
39 pause (1)
40 g3=ezplot(ynormal, [-15,15]);
41 text (3,3, ["y (Normal)=", string(ynormal)])
42 set (g3, 'color', 'c');
43 title("Tangent Line and Normal Line")
44
C Reset
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