How would you mathematically find the the max and min points of P ( x ) without graphing?

res2bfitjq

res2bfitjq

Answered question

2022-05-22

How would you mathematically find the the max and min points of P ( x ) without graphing?
P ( x ) = 5 sin ( π 6 x ) + 10 cos ( π 6 x ) + 11.2

Answer & Explanation

Dominique Holmes

Dominique Holmes

Beginner2022-05-23Added 10 answers

Assume that
cos   t = 5 5 2 + 10 2 ,   sin   t = 10 5 2 + 10 2
Hence
P ( t ) = 5 2 + 10 2 { cos   t sin   π x 6 + sin   t cos   π x 6 } + 11.2
= 5 5 sin   ( π x 6 + t ) + 11.2
That is max = 5 5 + 11.2 and min = 5 5 + 11.2

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