Maximum value of \(\displaystyle{\left({3}{\cos{{\left({x}-{0.730}\right)}}}-{3}\right)}^{{2}}\) Maximum value of

Frances Simon

Frances Simon

Answered question

2022-04-14

Maximum value of (3cos(x0.730)3)2
Maximum value of (3cos(x0.730) is 3 and minimum is -3
Conceptually , to find the maximum of (3cos(x0.730)3)2 is to use (33)2 however that is 0.But when I use the minimum value (33)2)=36 and 36 is the maximum value . But isn't this conceptually wrong to use the minimum value to find the maximum value ?
I do not understand why must we use -3 obviously squaring a negative number will give u a positive number . But is there a reason why must I use -3 ?

Answer & Explanation

shanna87mn

shanna87mn

Beginner2022-04-15Added 19 answers

You can think of (3cos(x0.730)3)2 as the square of the distance between 3cos(x0.730) and 3 And that distance will be maximized when 3cos(x0.730) is negative. And the square of the distance will always be minimized when the two coincide.

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