Search Colleges, Courses, Exams, Questions and Articles

Ask a query on 8879100846 Ask Login | Sign Up

 

 

› Ask & Answer › Question

If the slope of tangent to the curve y = ax3 – bx2 at x = 1 is equal to 3, where a ∈  [1,2] then number of possible integral values of b is

0 2 Views | Posted 3 weeks ago
Asked by Shiksha User

  • 1 Answer

  • V

    Answered by

    Vishal Baghel | Contributor-Level 10

    3 weeks ago

    d y d x = 3 a x 2 − 2 b x

    d y d x | x = 1 = 3 a − 2 b = 3

    a = 2 b + 3 3 ∈ [ 1 , 2 ]

    2 b + 3 ∈ [ 3 , 6 ]

    2 b ∈ [ 0 , 3 ]

    b ∈ [ 0 , 3 2 ]

Similar Questions for you

Curve y = 2x – x2, y(x) & y′(x) cut x-axis in M & N number of points respectively, find M + N.
A
alok kumar singh

y (x) = 2x – x2

y? (x) = 2x log 2 – 2x

M = 3

N = 2

M + N = 5

If the tangent to the curve y = x3 at the point P(t, t3) meets the curve again at Q, then the ordinate of the point which divides PQ internally in the ratio 1:2 is:
V
Vishal Baghel

y = x3

d y d x = 3 x 2 ⇒ d y d x | ( t , t 3 ) = 3 t 2

Equation of tangent y – t3 = 3t2 (x – t) 

Let again meet the curve at Q ( t 1 , t 1 3 )

⇒ t 1 3 − t 3 = 3 t 2 ( t 1 − t )

t 1 2 + t t 1 + t 2 = 3 t 2 [ ? t 1 ≠ t ]

t 1 2 + t t 1 − 2 t 2 = 0

=> t1 = -2t

Required ordinate = 2 t 3 + t 1 3 3 = 2 t 3 − 8 t 3 3 = − 2 t 3   

For x > 0, if f(x) = ∫ 1 x l o g e t ( 1 + t ) d t ,  then f(e) + f ( 1 e )  is equal to:
A
alok kumar singh

Given f(X) = ∫ 1 x l o g e t ( 1 + t ) d t . . . . . . . . . . . . ( i )  

So   f ( 1 x ) = ∫ 1 1 / x λ l o g e t 1 + t d t . . . . . . . . . . . . ( i i )

put t = 1 z       t h e n     d t = − 1 z 2 d z  

f ( 1 x ) = ∫ 1 x l o g e t t ( 1 + t ) d t . . . . . . . . . . . . ( i i i )

(i) + (iii), f(x) + f ( 1 x ) = ∫ 1 x ( l o g e t 1 + t + l o g e t t ( 1 + t ) ) d t

= [ ( l o g e t ) 2 2 ] 1 x = ( l o g x x ) 2 2

Hence f(e) + f ( 1 e ) = 1 2

Set of all possible values of k for which f(x) = sin x – cos x – kx + b decreases for all real values of x, is:
V
Vishal Baghel

f' (x) = cosx + sinx − k ≤ 0∀x ∈ R
k ≥ √2

The graph of function f(x) = x5/20 - x4/12 + 5 has :
V
Vishal Baghel

f (x) = x? /20 - x? /12 + 5
f' (x) = x? /4 - x³/3 = x³ (x/4 - 1/3)
Local maxima at 0, Local minima at 4/3
f' (x) = x³ - x² = x² (x-1)
x = 1 point of inflection

Get authentic answers from experts, students and alumni that you won't find anywhere else

Sign Up on Shiksha

On Shiksha, get access to

  • 65k Colleges
  • 1.2k Exams
  • 688k Reviews
  • 1800k Answers

Learn more about...

Share Your College Life Experience

Write a Review

Didn't find the answer you were looking for?

Search from Shiksha's 1 lakh+ Topics

or

Ask Current Students, Alumni & our Experts

Ask Now
Community GuidelinesUser Points System
QuestionsDiscussionsTags
×
×

This website uses Cookies and related technologies for the site to function correctly and securely, improve & personalise your browsing experience, analyse traffic, and support our marketing efforts and serve the Core Purpose. By continuing to browse the site, you agree to Privacy Policy and Cookie Policy.

Need guidance on career and education? Ask our experts

Characters 0/140

The Answer must contain atleast 20 characters.

Add more details

Characters 0/300

The Answer must contain atleast 20 characters.

Keep it short & simple. Type complete word. Avoid abusive language. Next

Your Question

Edit

Add relevant tags to get quick responses. Cancel Post