Find Equation of Tangent Line

Joined
Jun 27, 2021
Messages
5,386
Reaction score
422
Calculus
Section 3.1

Can you do 40 as a guide for me to do the rest?
Show steps along the way.

Thank you.

Screenshot_20220617-122328_Samsung Notes.jpg
 
40.

y=x^(1/4) -x at point (1,0)

first find the slope of tangent line

(dy/dx)(x^(1/4) -x )= 1/(4x^(3/4)) - 1

compute the slope at point (1,0)

m=1/(4*1^(3/4)) - 1= -3/4

so far, tangent line is: y= -(3/4)x +b

use point to calculate b:

0= -(3/4)1+b

0+3/4=b

b=3/4

tangent line is: y=-(3/4)x+3/4
upload_2022-6-17_15-31-20.png




 
40.

y=x^(1/4) -x at point (1,0)

first find the slope of tangent line

(dy/dx)(x^(1/4) -x )= 1/(4x^(3/4)) - 1

compute the slope at point (1,0)

m=1/(4*1^(3/4)) - 1= -3/4

so far, tangent line is: y= -(3/4)x +b

use point to calculate b:

0= -(3/4)1+b

0+3/4=b

b=3/4

tangent line is: y=-(3/4)x+3/4
View attachment 3561



Easy enough when you provide steps as you did here.
 
40.

y=x^(1/4) -x at point (1,0)

first find the slope of tangent line

(dy/dx)(x^(1/4) -x )= 1/(4x^(3/4)) - 1

compute the slope at point (1,0)

m=1/(4*1^(3/4)) - 1= -3/4

so far, tangent line is: y= -(3/4)x +b

use point to calculate b:

0= -(3/4)1+b

0+3/4=b

b=3/4

tangent line is: y=-(3/4)x+3/4
View attachment 3561




IMG_20220618_173842.jpg


Can you check my work for the three unanswered calculus threads?
 

Members online

No members online now.

Trending content

Forum statistics

Threads
2,531
Messages
9,860
Members
697
Latest member
lemon in icewine
Back
Top