If f(x)={{:(1/absx,,absxge1),(ax^2+b, ,a...

If `f(x)={{:(1/absx,,absxge1),(ax^2+b, ,absxlt1):}`is differentiable at every point of the domain,then the values of a and b are respectively :

A

`1/2,- 3/2`

B

`5/2, - 3/2`

C

`1/2,1/2`

D

`- 1/2, 3/2`

Text Solution

AI Generated Solution

Topper's Solved these Questions

JEE MAIN 2021
JEE MAINS PREVIOUS YEAR|Exercise MATHEMATICS SECTION B|20 Videos
JEE MAIN 2021
JEE MAINS PREVIOUS YEAR|Exercise Mathematic section A|20 Videos
JEE MAIN 2021
JEE MAINS PREVIOUS YEAR|Exercise MATHEMATICS (SECTION B)|30 Videos
JEE MAIN
JEE MAINS PREVIOUS YEAR|Exercise QUESTION|1 Videos
JEE MAIN 2022
JEE MAINS PREVIOUS YEAR|Exercise Question|454 Videos

Similar Questions

Explore conceptually related problems

If f(x)={{:(a+cos^(-1)(x+b),":",xge1),(-x,":",xlt1):} is differentiable at x = 1, then the value of b-a is equal to

If ax^(2)+bx+4 attains its minimum value -1 at x = 1, then the values of a and b are respectively

If x^(2)-x+1 is a factor of x^(4)+ax^(2)+b , then the values of a and b are respectively _______.

f(x)={(1/absx,,absx ge1 ),(ax^2+b,,absxlt1):} Find the possible value of a and b given that f(x) is differentiable at x=1

If f(x)={{:(,ax^(2)-b,|x|lt 1),(,(1)/(|x|),|x| ge1):} is differentiable at x=1, then

If the function f(x) = {(5x-4, ",","if"0 lt x le 1),(4x^(2)+3bx, ",", "if"1 lt x le 2 ):} is continuous at every point of its domain, then the value of b is

If x^(2)+x+1 is a factor of x^(4)+ax^(2)+b , then the values of a and b , respectively are ______.

If f(x)={[ax+b;,xle-1],[ax^(4)+x^(2)+3b;,xgt-1]} is differentiable for all x in R then (a+2b) is equal to

If lim_(xrarr0)(axe^(x)-b log(1+x))/(x^(2))=3 , then the value of a and b are respectively.

JEE MAINS PREVIOUS YEAR-JEE MAIN 2021-MATHEMATICS SECTION A

1/(3^2 -1)+1/(5^2 -1)+1/(7^2 -1)+……+1/((201)^2 -1) is equal to
Text Solution
|
The values of x in (0, pi) satisfying the equation. |{:(1+"sin"^(2)...
Text Solution
|
If f(x)={{:(1/absx,,absxge1),(ax^2+b, ,absxlt1):}is differentiable at ...
Text Solution
|
The integral int((2x-1)cossqrt((2x-1)^2+5))/(sqrt(4x^2-4x+6))dx is equ...
Text Solution
|
Choose the correct statement about two circles whose equations are giv...
Text Solution
|
The equation of one of the straight lines which passes through the poi...
Text Solution
|
The number of integral values of m so the abscissa of point of interse...
Text Solution
|
Let alpha,beta,gamma are the real roots of the equation x^3+a x^2+b x+...
Text Solution
|
The real valued function f(x)=(cosec^(-1)x)/(sqrt(x-[x])), where [x] d...
Text Solution
|
The value of is equal to
Text Solution
|
Let A+2B=[(1,2,0),(6,-1,3),(-5,3,1)] and 2A-B=[(2,-1,5),(2,-1,6),(0,1,...
Text Solution
|
If lim(xto0)(sin^(-1)x-tan^(-1)x)/(3x^3) is equal to L, then the value...
Text Solution
|
A vector veca has components 3p and 1 with rrespect to a rectangular c...
Text Solution
|
If alpha,beta are natural numbers such that 100^(alpha)-199beta=(100)(...
Text Solution
|
If the equation aabsz^2+bar(baralphaz+alphabarz)+d=0 represents a ci...
Text Solution
|
The differential equation satisfied by the system of parabolas y^2=4a(...
Text Solution
|
Let (1+x+2x^2)^20=a0+a1x+a2x^2+....+a40x^40. " Then, "a1+a3+a5.....+a3...
Text Solution
|
The sum of all the 4-digit distinct numbers that can be formed with th...
Text Solution
|
If the functions are defined as f(x)=sqrtx and g(x) = sqrt(1-x), then ...
Text Solution
|
For the four circles M, N, O and P, following four equations are given...
Text Solution
|