I do not have any idea to deal with this question, can anyone help?
It is given that
,
where 0 <= x <= 2x.
If y has the maximum value when x =
and the minimum value when x = ,
find the values of and .
Notice if and you have expression,Originally Posted by ling_c_0202
, then, do the following trick,
Think, of a right triangle with legs then its hypotenuse is thus, if is an angle between the hypotenuse and then you have,
Thus, substituting that into our expression,
Thus, sum for sine of two angles,
where
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Let us return back to your problem.
You have thus, using this trick you have,
where
As explained before the max occurs when,
Thus,
Thus,
Thus,
We need,
Which is,
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For the min that happens when,
Thus,
Thus,
Thus,
But you need,
But,
Thus,