Let f(x)=sin^(3)x+k sin^(2)x,-(pi)/(2) l...

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

Verified by Experts

The correct Answer is:

`-(3)/(2) lt k lt (3)/(2)`

Similar Questions

Explore conceptually related problems

Let f(x)=sin^(4)x-cos^(4)x int_(0)^((pi)/(2))f(x)dx =

Let f(x) = |x|+|sin x|, x in (-pi/2, (3pi)/2) . Then, f is :

Find the intervals in which the function f given by f(x)=sin x + cos x(0 le x le 2 pi) is decreasing

Find the intervals in which the function f given by f(x)=sin x + cos x(0 le x le 2 pi) is increasing

Find the intervals in which the function f(x)=sin x-cos x where 0 lt x lt 2pi is decreasing.

Find the intervals in which the function f(x)=sin x-cos x where 0 lt x lt 2pi is increasing.

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

If f(x)=sin^2x+sin^2(x+pi/3)+cos x.cos(x+pi/3) and g(5/4)=1 , then

If f(x)={x^2 sin((pi x)/2), |x| =1 then f(x) is

If - pi/2 lt x lt pi/2 , then the range of the function f(x)=cos [x] is