Find Equation of Tangent Line...2

[nycmathguy]

Calculus
Section 3.1

Can you do 44 as a guide for me to do 43?
Show steps along the way.

Thank you.

 

[MathLover1]

44.

y=x-sqrt(x) at point (1,0)

first find the slope of tangent line

(dy/dx)(x-sqrt(x) )=1-1/(2sqrt(x))

compute the slope at point (1,0)

m=1-1/(2sqrt(1))=1-1/2=1/2

so far, tangent line is: y=(1/2)x +b

use point to calculate b:

0=(1/2)1+b

0=1/2+b

b=-1/2


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

 

[nycmathguy]

44.

y=x-sqrt(x) at point (1,0)

first find the slope of tangent line

(dy/dx)(x-sqrt(x) )=1-1/(2sqrt(x))

compute the slope at point (1,0)

m=1-1/(2sqrt(1))=1-1/2=1/2

so far, tangent line is: y=(1/2)x +b

use point to calculate b:

0=(1/2)1+b

0=1/2+b

b=-1/2


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

View attachment 3559

Another easy step by step reply makes this a walk in the park.

 

[nycmathguy]

44.

y=x-sqrt(x) at point (1,0)

first find the slope of tangent line

(dy/dx)(x-sqrt(x) )=1-1/(2sqrt(x))

compute the slope at point (1,0)

m=1-1/(2sqrt(1))=1-1/2=1/2

so far, tangent line is: y=(1/2)x +b

use point to calculate b:

0=(1/2)1+b

0=1/2+b

b=-1/2


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

View attachment 3559

 

[MathLover1]

correct

 

[nycmathguy]

correct

View attachment 3589

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