Home
Class 12
MATHS
Let f(x)=sin^3x+lambdasin^2x ,pi/2<x<pi/...

Let `f(x)`=`sin^3x+lambdasin^2x` ,`pi/2`<`x`<`pi/2dot` Find the intervals in which `lambda` should lie in order that `f(x)` has exactly one minimum and exactly one maximum.

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(x)=sin^3x+lambda sin^2x , -pi/2 < x < pi/2 Find the intervals in which lambda should lie in order that f(x) has exactly one minimum and exactly one maximum.

Let f(x)=2sin^(3)x+lamdasin^(2)x,-(pi)/2ltxlt(pi)/2 . If f(x) has exactly one minimum and one maximum, then lamda cannot be equal to

Let f(x)=-sin^3x+3sin^2x+5 on [0,pi/2] . Find the local maximum and local minimum of f(x)dot

Let f(x)={(1-sin^3x)/(3cos^2x) if x pi/2 find a and b. .

Separate the intervals of monotonocity of the function: f(x)=-sin^3x+3sin^2x+5,x in [-pi/2,pi/2]dot

Let f(x)=sinx+2cos^2x , x in [pi/6,(2pi)/3] , then maximum value of f(x) is

Let f(x) = sin^(3)x - 3 sinx + 6, AA x in (0, pi) .The number of local maximum/maxima of the function f(x) is

Let f(x)=|x|+|sin x|, x in (-pi//2,pi//2). Then, f is

The period of the function f(x)=c^((sin^2x) +sin^2 (x+pi/3)+cosxcos(x+pi/3)) is (where c is constant)

Statement 1: Let f(x)=sin(cos x) \ i n \ [0,pi/2] . Then f(x) is decreasing in [0,pi/2] Statement 2: cosx is a decreasing function AAx in [0,pi/2]