1.Directions:To receive credit, write neatly and show all work. All answers are

Question

1.Directions:To receive credit, write neatly and show all work. All answers are to be exact expres ons, not their decimal approxi not1.732 and n, not 3.1416 and fully simplified circle your answers. No credit for answers not pported by explanatory work or Answers alone have no value. Submit homework on this sheet of paper only work must be done using methods studied in this co sections indicated, not of any subsequent sections. 1. Let y Give a complete discussion of the curve covering each of the points below. (x-1)2 a) Domain b) Intercepts c) Asymptotes (find equations and identify as vertical or horizontal) d) First derivative: make the table, find intervals of increase/decrease, and both coordinates of any local extrema

Explanation / Answer

From the given question,

y= x/(x-1)2

(a)Domain are all values except x=1

R - {1}

(b) Intercepts

to find x-intercept, replace y=0

0=x/(x-1)2

x=0

to find y-intercept, replace x=0

y= 0/(0-1)2

y=0

both x-intercept and y-intercept are aero.

(c) asymptotes

to find vertical asymptote, replace denominator =0

x-1=0

x=1

vertical asymptote is x=1

to find horizontal asymptote,

y= x/(x-1)2

dividing numerator and denominator by x2

y= (1/x)/(1/x -1)2 =infinity

so, there is no horizontal asymptote.

(d)y= x/(x-1)2

dy/dx= [(x-1)2 d/dx (x) - x d/dx (x-1)2]/ (x-1)4

= [(x-1)2 -2x(x-1)]/ (x-1)4

=(x-1)(x-1-2x)/(x-1)4

=(x-1)(-x-1)/(x-1)4

=-(x+1)/(x-1)3

for increasing function, dy/dx>0

-(x+1)/(x-1)3 >0

function is increasing -1<x<1

function is decreasing x<-1 ans x>1

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.