Let f(x)=int0^x (cost)/tdt Then at x=(2n...

Let `f(x)=int_0^x (cost)/tdt` Then at `x=(2n+1)pi/2` f(x) has

maxima when n=-2,-4,-6,.. and minima when n=-1,3,-5,..

maxima when n=-1,-3,-5,… and minima when n=1,3,5,…

minima when n=0,2,4,… and maxima when n=1,3,5,…

none of these

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

MAXIMA AND MINIMA
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos
MAXIMA AND MINIMA
OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|7 Videos
MATHEMATICAL REASONING
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|20 Videos
MEASURES OF CENTRAL TENDENCY
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|21 Videos

Similar Questions

Explore conceptually related problems

A function f is continuous for all x (and not everywhere zero) such that f^2(x)=int_0^xf(t)(cost)/(2+sint)dtdot Then f(x) is (a) 1/2 1n((x+cosx)/2); x!=0 (b) 1/2 1n(3/(x+cosx)); x!=0 (c) 1/2 1n((2+sinx)/2); x!=npi,n in I (d) (cosx+sinx)/(2+sinx); x!=npi+(3pi)/4,n in I

If f(x)=int_0^x(sint)/t dt ,x >0, then (a) f(x) has a local maxima at x=npi(n=2k ,k in I^+) (b) f(x) has a local minima at x=npi(n=2k ,k in I^+) (c) f(x) has neither maxima nor minima at x=npi(n in I^+) (d) (f)x has local maxima at x=npi(n=2k -1, k in I^+)

If f(x)=-int_(0)^(x) log (cos t) dt, then the value of f(x)-2f((pi)/(4)+(x)/(2))+2f((pi)/(4)-(x)/(2)) is equal to

Let f(x) be a continuous and differentiable function such that f(x)=int_0^xsin(t^2-t+x)dt Then prove that f^('')(x)+f(x)=cosx^2+2xsinx^2

If f(x) = int_(0)^(x^(2)) sqrt(cost)dt , find f'(x)

If f(x)=int_0^x("cos"(sint)+"cos"(cost)dt , then f(x+pi) is (a) f(x)+f(pi) (b) f(x)+2(pi) (c) f(x)+f(pi/2) (d) f(x)+2f(pi/2)

If f(x)=int_0^x("cos"(sint)+"cos"(cost)dt ,t h e nf(x+pi)i s (a) f(x)+f(pi) (b) f(x)+2(pi) (c) f(x)+f(pi/2) (d) f(x)+2f(pi/2)

Let f(x) =int_1^x e^t/tdt,x in R^+ . Then complete set of valuesof x for which f(x) leq In x is

If f(x)=int_0^x e^(cost)/(e^(cost)+e^-(cost))dt , then 2f(pi)= (A) 0 (B) pi (C) -pi (D) none of these

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=

OBJECTIVE RD SHARMA ENGLISH-MAXIMA AND MINIMA -Exercise

The greatest value of f(x)=cos(x e^([x])+7x^2-3x),x in [-1,oo], is (wh...
Text Solution
|
The points of extremum of phi (x)=int(1)^(x)e^(-t^(2//2)) (1-t^(2)) dt...
Text Solution
|
Let f(x)=int0^x (cost)/tdt Then at x=(2n+1)pi/2 f(x) has
Text Solution
|
It is given that at x=1 , the function x^4-62 x^2+a x+9 attains its ma...
Text Solution
|
The minimum value of (1+1/(sin^nalpha))(1+1/(cos^nalpha)) is
Text Solution
|
The minimum value of (x-a)(x-b) is
Text Solution
|
The altitude of a right circular cone of minimum volume circumscired a...
Text Solution
|
If (x-a)^(2m) (x-b)^(2n+1), where m and n are positive integers and a...
Text Solution
|
If (x-a)^(2m) (x-b)^(2n+1), where m and n are positive integers and a...
Text Solution
|
In a triangleA B C ,/B=90^0 and b+a=4. The area of the triangle is ma...
Text Solution
|
The function f(x) given by f(x)=|{:(x-1", "x+1", "2x+1),(x+1", ...
Text Solution
|
Maximum area of a reactangle which can be inscribed in a circle of a...
Text Solution
|
If f(x)={:{(3x^2+12x-1"," -1le x le2),(37-x ","2 lt x le 3):} then
Text Solution
|
The perimeter of a sector is p. The area of the sector is maximum when...
Text Solution
|
If a^(2)x^(4)b^(2)y^(4)=c^(6)(a,b,x,y,cgt0) then the maximum value of ...
Text Solution
|
The function int(-1)^(x)t(e^t-1)(t-1)(t-2)^3(t-3)^5dt has local mini...
Text Solution
|
Let f(x) be a function such that f'(a) ne 0 . Then , at x=a, f(x)
Text Solution
|
Let a,b,c be positive real parameter and ax^2+ b/x^2gec, AA xepsilonR ...
Text Solution
|
If xy=a^2 and S = b^2x + c^2y where a, b and c are constants then the ...
Text Solution
|
Let f(x)=e^x sinx , slope of the curve y=f(x) is maximum at x=a if 'a'...
Text Solution
|