Find Equation of Tangent Line

Calculus
Section 3.1

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

Thank you.

 

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

 

Easy enough when you provide steps as you did here.

 

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

 

correct

 

Very nice. Better than being wrong again. See below.

Differentiate...2