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JEE Main20245 Apr 2024Evening ShiftMathematicsApplication of DerivativesActual

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 _________

Correct answer

0

Step-by-step solution

aligned & (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 aligned aligned & m=9 & M=41 & M^2-m^2=41^2-9^2=1600 aligned

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