UrbanPro
true

Take Class 12 Tuition from the Best Tutors

  • Affordable fees
  • 1-1 or Group class
  • Flexible Timings
  • Verified Tutors

Stationary point

Sameer Ninawe
17/03/2017 0 0

Find the stationary point for the curve y = x3 – 3x2 + 3x – 3, and its type.

y = x3 – 3x2 + 3x – 3

dy/dx = 3x2 – 6x + 3

= 3(x2 – 2x + 1)

= 3(x – 1)2

dy/dx = 3(x – 1)2  = 0

doubleright x = 1

When x = 1, y = 13 – 3×12 + 3×1 – 3

= 1 – 3 + 3 – 3  =  -2

(1, -2) is a stationary point.

To determine it type, check dy/dx or y’ around x = 1.

x 0 (LHS) 1 2 (RHS)
dy/dx 3(-1)2 = 3 >0 0 3(1)2 = 3 >0
Curve Increasing Stationary Increasing

 

Since the curve is increasing on both sides of (1, -2), the curve is monotonic increasing.
And (1, -2) is a point of horizontal inflection.

0 Dislike
Follow 0

Please Enter a comment

Submit

Other Lessons for You


Solution to a trigonometric problem requested by one student
∫ sin 4x cos 2x dx as we don't have any ready made formulae for product of function in integration, let's split it into sum or difference. sin A cos B = 1/2 {sin (A + B ) + sin ( A - B )} A=...



Rigid body and Centre of mass
Till now, we have considered the motion of a single particle or a body considered as a particle represented as a point mass (practically no size) and various laws were applied on them. But ant real body...
X

Looking for Class 12 Tuition Classes?

The best tutors for Class 12 Tuition Classes are on UrbanPro

  • Select the best Tutor
  • Book & Attend a Free Demo
  • Pay and start Learning

Take Class 12 Tuition with the Best Tutors

The best Tutors for Class 12 Tuition Classes are on UrbanPro

This website uses cookies

We use cookies to improve user experience. Choose what cookies you allow us to use. You can read more about our Cookie Policy in our Privacy Policy

Accept All
Decline All

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 55 lakh students rely on UrbanPro.com, to fulfill their learning requirements across 1,000+ categories. Using UrbanPro.com, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 7.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on UrbanPro.com. Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more