In a video lecture which is related to inequalities chapter.......for an example problem g(x)=|x-2|+|x-3|+|x-6|. find the least possible value of g(x)....it has been in the second step of the solution that 2

Question

In a video lecture which is related to inequalities chapter.......for an example problem g(x)=|x-2|+|x-3|+|x-6|. find the least possible value of g(x)....it has been in the second step of the solution that 2<=x<=3, g(x)=7-x, minimum at x=3 and g(x)=4....please explain me about this step and other steps also.......thank you

KUPPA V U KARTHIK · Answer

thanks alot for the explanation..........:)

PRACHI AWASTHI · Answer

Since,2<=x<=3so minimum value of x can be 2 and maximum can we 3so for x=2,g(x)= |2-2|+|2-3|+|2-6|     (since |-n|=n)=0+1+4=5so for x=2 g(x)=5
similarly for x=3;
g(x)= 1+0+3=4so for x=3 g(x)=4
HENCE LEAST VALUE OF g(x) CAN BE 4

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