A) 1
B) 5
C) 4
D) 9
Correct Answer: A
Solution :
\[f(x)=2{{x}^{3}}-9{{x}^{2}}+12x+5\] \[f'(x)=6{{x}^{2}}-18x+12=0\] \[\Rightarrow \]\[{{x}^{2}}-3x+2=0\] \[x=1\]or \[x=2\] \[f''(x)=12x-18\] \[f''(1)=12(1)-18=-6<0\] Hence, function has maxima at \[x=1\] \[\Rightarrow \]\[M=f(1)=2-9+12+5=10\] \[f''(2)=12(2)-18=6>0\] Hence, function has minima at \[x=2\] \[\Rightarrow \]\[m=f(2)=2(8)-9(4)+12(2)+5=9\] Therefore, \[M-m=10-9=1\] Answer is option A.You need to login to perform this action.
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