# Equation of Tangent Line and Normal Line

Discussion in 'Calculus' started by nycmathguy, Jun 17, 2022.

1. ### nycmathguy

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Calculus
Section 3.1

Can you do 42 as a guide for me to do 41?
Show steps along the way.

Thank you.

nycmathguy, Jun 17, 2022

2. ### MathLover1

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42.

y=x^(2/3) at point (1,1)

first find the slope of tangent line

(dy/dx)(x^(2/3))= 2/(3x^(1/3))

compute the slope at point (1,1)

m=2/(3*1^(1/3))=2/3

so far, tangent line is: y=(2/3)x +b

use point to calculate b:

1=(2/3)1+b

1=2/3+b

b=1-2/3
b=1/3

tangent line is: y=(2/3)x+1/3

MathLover1, Jun 17, 2022
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3. ### nycmathguy

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Nice graphing work. Which line is the normal line?

nycmathguy, Jun 18, 2022
4. ### MathLover1

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opss, I didn't do normal line

if the slope of tangent line is (2/3) , the slope of a normal line is negative reciprocal -3/2

use point-slope formula

y-y1=m (x-x1) ..........given point is (1,1)

y-1=-(3/2)(x-1)
y-1=-(3/2)x+3/2
y=-(3/2)x+3/2 +1
y=-(3/2)x+5/2

Last edited: Jun 18, 2022
MathLover1, Jun 18, 2022
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5. ### nycmathguy

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Much better. In what way do the normal line and tangent line relate?

nycmathguy, Jun 18, 2022
6. ### MathLover1

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as I stated above, the slope of tangent line and the slope of a normal line are negative reciprocal to each other

MathLover1, Jun 18, 2022
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7. ### nycmathguy

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Ok. Thanks. Interesting.

nycmathguy, Jun 18, 2022
8. ### nycmathguy

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Can you provide the graph of both lines on the xy-plane?

nycmathguy, Jun 18, 2022
9. ### MathLover1

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MathLover1, Jun 18, 2022
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10. ### nycmathguy

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I assume my answer is correct. Yes?

nycmathguy, Jun 18, 2022
11. ### MathLover1

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yes it is correct

MathLover1, Jun 19, 2022
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12. ### nycmathguy

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Perfect. We move on to Section 3.2 aka the Product Rule and Quotient Rule. I haven't decided if to go back to the Riegelmann Boardwalk at Coney Island or try Prospect Park today. Something is pulling me toward the park.

Either way, I gotta go outside and take advantage of this heavenly day. By "heavenly day" I mean windy, sunny and low humidity. My weekend is almost over. Life sucks!! Too much at the job and very little time for the things I like to do.

nycmathguy, Jun 19, 2022