Let the maximum and minimum values of ( 8 x − x 2 − 12 − 4 ) 2 + ( x − 7 ) 2 , x ∈ R be M and m , respectively. Then M 2 − m 2 is equal to _________

Question

Let the maximum and minimum values of ( 8 x − x 2 − 12 ​ − 4 ) 2 + ( x − 7 ) 2 , x ∈ R be M and m , respectively. Then M 2 − m 2 is equal to _________

TestHub · Accepted Answer

​ ( x − 7 ) 2 + ( y − 4 ) 2 y = 8 x − x 2 − 12 ​ y 2 = − ( x − 4 ) 2 + 16 − 12 ( x − 4 ) 2 + y 2 = 4 ​ ​ m = 9 M = 41 M 2 − m 2 = 4 1 2 − 9 2 = 1600 ​

Mathematics - Application of Derivative Question with Solution | TestHub

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