L e tf(x)={|x^2-3x|+a ,0lt=x<3/2-2x+3,xg...

`L e tf(x)={|x^2-3x|+a ,0lt=x<3/2-2x+3,xgeq3/2` If `f(x)` has a local maxima at `x=3/2` , then greatest value of `|4a|` is _________

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Verified by Experts

The correct Answer is:

-2.25

`f(3/2)=0underset(xrarr3/2)lim|x^(2)-3x|+ale0 or ale-9/4`
Hence greatest value of a is -2.25

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