Find the minimum and maximum value of function:
$y = \sin^{2} x - \sin x * \cos x$

Question

Find the minimum and maximum value of function:  y  =      sin          2        ⁡  x  −  sin  ⁡  x  ∗  cos  ⁡  x

abortargy · Accepted Answer

Find the minimum and maximum value of function:

y = \sin^{2} x - \sin x * \cos x

Your going to want to take the first and second derivatives tofind the max and min values.

y = (\sin x) (\sin x) - (\sin x) (\cos x)

y^{'} = (\sin x) (\cos x) + (\cos x) (\sin x) + (\cos x) (\cos x) + (\sin x) (- \sin x)

y^{'} = 2 (\sin x) (\cos x) - \sin^{2} x + \cos^{2} x

y^{″} = 2 (\cos x) (\cos x) + 2 (\sin x) (- \sin x) - 2 (\sin x) (\cos x) - 2 (\sin x) (\cos x)

y^{″} = 2 \cos^{2} x - 2 \sin^{2} x - 4 (\sin x) (\cos x)

When you find the second derivative, find x to where y = 0,these are the inflection points where max and min values occur. Then take those values for x and plus them into the original y equation to find the max and min values of the function.

Find the minimum and maximum value of function: y = sin^2 x - sinx*cosx

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