InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Let `f(x) = sin^6x + cos^6x + k(sin^4 x + cos^4 x)` for some real number k. Determine(a) all real numbers k for which `f(x)` is constant for all values of x.A. [-1,0]B. `[0,1/2]`C. `[-1,-1/2]`D. None of these |
|
Answer» Correct Answer - C f(x)=0 `rArr (1-3 ) sin^2 x cos^2 x)+k[1-2 sin^2 x cos^2 x]=0` `rArr K+1 =(sin ^2 x cos^2 x)/(1-2 sin^2x cos^2x)` `rArrk=(3sin^2xcos^2x-1)/(1-2sin^2xcos^2x)` `=-3/2(1-2sin^2xcos^2x-1/3)/(1-2sin^2xcos^2x)` `=-3/2(1-(1/3)/(1-2sin^2xcos^2x))` minimum of `sin^2xcos^2x " is 0 at " x=0,pi//2` Maximum of `sin^2xcos^2x" is "1//4" at " x=pi//2` Hence, k in[1,-1/2] |
|