Let a, b R be such that the function f ...

Let a, b R be such that the function f given by `f(x)""=""ln""|x|""+""b x^2+""a x ,""x!=0` has extreme values at `x""=""1` and `x""=""2` . Statement 1: f has local maximum at `x""=""1` and at `x""=""2` . Statement 2: `a""=1/2"and"b=(-1)/4` (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

APPLICATIONS OF DERIVATIVES
MCGROW HILL PUBLICATION|Exercise Question for Previous Year.s B-Architecture Entrance Examination Papers|27 Videos
APPLICATIONS OF DERIVATIVES
MCGROW HILL PUBLICATION|Exercise Exercise ( NUMERICAL ANSWER TYPE QUESTIONS)|17 Videos
AREA BY INTEGRATION
MCGROW HILL PUBLICATION|Exercise Question from Previous Years. B-Architecture Entrance Examination Papers|12 Videos

Similar Questions

Explore conceptually related problems

Consider the function f(x)=|x^2|+|x^5|,x in R . Statement 1: f'(4)=0 Statement 2: f is continuous in [2, 5], differentiable in (2, 5) and f(2) = f(5). (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

Let A be a 2""xx""2 matrix Statement 1 : a d j""(a d j""A)""=""A Statement 2 : |a d j""A|""=""|A| (1) Statement1 is true, Statement2 is true, Statement2 is a correct explanation for statement1 (2) Statement1 is true, Statement2 is true; Statement2 is not a correct explanation for statement1. (3) Statement1 is true, statement2 is false. (4) Statement1 is false, Statement2 is true

Let x_1,""x_2,"". . . . . . ,""x_n be n observations, and let bar x be their arithematic mean and sigma^2 be their variance. Statement 1: Variance of 2x_1,""2x_2,"". . . . . . ,""2x_n""i s""4""sigma^2 . Statement 2: Arithmetic mean of 2x_1,""2x_2,"". . . . . . ,""2x_n""i s""4x . (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

Statement 1: An equation of a common tangent to the parabola y^2=16sqrt(3)x and the ellipse 2x^2+""y^2=""4""i s""y""=""2x""+""2sqrt(3) . Statement 2: If the line y""=""m x""+(4sqrt(3))/m ,(m!=0) is a common tangent to the parabola y^2=""16sqrt(3)x and the ellipse 2x^2+""y^2=""4 , then m satisfies m^4+""2m^2=""24 . (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

Statement 1: (lim)_(x->0)sin^(-1){x}\ does not exist (where {.} denotes fractional part function). Statement 2: {x} is discontinuous at x=0 (a)Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 (b)Statement 1 is true, Statement 2 is true; Statement 2 not a correct explanation for statement 1. (c)Statement 1 is true, statement 2 is false (d)Statement 1 is false, statement 2 is true

Let f(x)=x|x| and g(x)=s in x Statement 1 : gof is differentiable at x=0 and its derivative is continuous at that point Statement 2: gof is twice differentiable at x=0 (1) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for statement 1 (2) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for statement 1. (3) Statement 1 is true, statement 2 is false. (4) Statement 1 is false, Statement 2 is true

9, Let A be a 2 x 2 matrix with real entries. Let I be the 2 × 2 2identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that A2 -1 nvo bud o malai Statement 1: If A 1 and A?-1, then det A =-1. Statement 2: If A 1 and A?-I, then tr (A)?0 A. Statement 1 is false, statement 2 is true. B. Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 . C. Statement 1 is true, statement 2 is true; statement 2 is nota correct explanation for statement 1. D. Statement 1 is true, statement 2 is false.

Statement 1: The function f(x)=[[x]]-2[x-1]+[x+2] is discontinuous at all integers. Statement 2: [x] is discontinuous at all integral values of xdot Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true; Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true

Statement 1: The value of the integral int_(pi//6)^(pi//3)(dx)/(1+sqrt(tanx)) is equal to pi/6 Statement 2: int_a^bf(x)dx=int_a^bf(a+b-x)dxdot Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true; Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true

Statement 1: sum_(r=0)^n(r+1)^n c_r=(n+2)2^(n-1)dot Statement 2: sum_(r=0)^n(r+1)^n c_r=(1+x)^n+n x(1+x)^(n-1)dot (1) Statement 1 is false, Statement ( 2) (3)-2( 4) is true (6) Statement 1 is true, Statement ( 7) (8)-2( 9) (10) is true, Statement ( 11) (12)-2( 13) is a correct explanation for Statement 1 (15) Statement 1 is true, Statement ( 16) (17)-2( 18) (19) is true; Statement ( 20) (21)-2( 22) is not a correct explanation for Statement 1. (24) Statement 1 is true, Statement ( 25) (26)-2( 27) is false.

MCGROW HILL PUBLICATION-APPLICATIONS OF DERIVATIVES-Question for Previous Year.s AIEEE/JEE Main Paper

The curve that passes through the point (2, 3) and has the property ...
Text Solution
|
Let be a function defined by f(x)={{:(tanx/x", "x ne0),(1", "x...
Text Solution
|
Let a, b R be such that the function f given by f(x)""=""ln""|x|""+""...
Text Solution
|
A spherical balloon is filled with 4500p cubic meters of helium gas...
Text Solution
|
The cost of running a bus from A to B, is Rs. (av + b/v), where v km/h...
Text Solution
|
If the surface area of a sphere of radius r is increasing uniformly at...
Text Solution
|
The real number k for which the equation, 2x^3+""3x""+""k""=""0 has tw...
Text Solution
|
The maximum area of a right angled triangle with hypotenuse h is
Text Solution
|
Statement-1: The equation x log x= 2-x is satisfied by at least one va...
Text Solution
|
Statement 1 : The function x^2 (e^x+e^-x) is increasing for all x> 0 S...
Text Solution
|
If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...
Text Solution
|
If x = -1 and x = 2 are extreme points of f(x) = alpha log|x| + beta x...
Text Solution
|
If the volume of a sphere increase at the rate of , 2pi cm^(3)//sec, ...
Text Solution
|
If non-zero real number b and c are such that min f(x) gt max g(x) whe...
Text Solution
|
Let f'(x) gt0 and g'(x) lt 0 " for all " x in R Then
Text Solution
|
If Rolle's theorem holds for the function f(x) = 2x^(3) + ax^(2) + bx ...
Text Solution
|
Let f(x) be a polynomial of degree four having extreme values at x"...
Text Solution
|
The equation of a normal to the curve, sin y = x (sinpi/3+y)at x=0 is
Text Solution
|
Let k and K be the minimum and the maximum values of the function f(x)...
Text Solution
|
From the top of a 64 metres high tower, a stone is thrown upward verti...
Text Solution
|