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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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CENGAGE-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Exercise (Numerical)
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  3. Let f(x)={{:(|x^(3)+x^(2)+3x+sinx(3+sin(1)/(x)), x ne 0), (0,x=0):} ...

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  4. Leg f(x) be a cubic polynomial which has local maximum at x=-1a n df(x...

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  5. consider P(x) to be a polynomial of degree 5 having extremum at x=-1,1...

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  6. If m is the minimum value of f(x , y)=x^2-4x+y^2+6y when xa n dy are s...

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  7. For a cubic function y=f(x),f^(x)=4x at each point (x , y) on it and i...

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  10. The number of nonzero integral values of a for which the function f(x)...

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  11. L egf(x)={x^(3/5),ifxlt=1-(x-2)^3,ifx >1 Then the number of critical ...

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  13. A rectangle with one side lying along the x-axis is to be inscribed in...

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  14. The least integral value of x where f(x)=(log)(1/2)(x^2-2x-3) is monot...

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  15. The least area of a circle circumscribing any right triangle of area 9...

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  16. L e tf(x)={|x^2-3x|+a ,0lt=x<3/2-2x+3,xgeq3/2 If f(x) has a local max...

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  17. Let f(x)=30-2x -x^3, the number ofthe positive integral values of x wh...

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  18. Let f(x) ={{:(x(x-1)(x-2),(0lexltn),sin(pix),(nlexle2n):} least valu...

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  19. Number of critical point of the function f(X) =x+sqrt(|x|) is .

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  20. consider f(X) =(1)/(1+|x|)+(1)/(1+|x-1|) Let x(1) and x(2) be point wh...

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