InterviewSolution
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InterviewSolution
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Let `f(x)=-sin^3x+3sin^2x+5on[0,pi/2]`. Find the local maximum and local minimum of `f(x)dot` |
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Answer» Correct Answer - Strictly increasing f(x) =-`sin^(3) x + 3 sin^(2) x+5` `therefore f(X) =-3 cos x sin^(2) + 6 sinxcos x` Now `sin x -2 lt 0 forall x in [0,(pi)/(2)]` sinx cos `x ge 0 forall x in [0,(pi)/(2)]` Thus f(x) is a strictly incresing function `forall x in [0,pi//2]` Hence f(x) is minimum when x=0 and maximum when `x =pi//2` `f_(min)=f(0)=5` `f_(max)=f(pi//2)=7` |
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