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The absolute maximum and minimum values of functions can be found by their monotonic and asymptotic behaviour provided they exist. We may agree that finite limits values may be reagarded as absolute maximum or minimum. For instance the absolute maximum value of `(1)/(1+x^(2))` is unity. It is attained at x=0 while absolute maximum value of the same functions is zero which is a limiting value of `(xrarrooorxrarr-oo)`
The function `x^(4)-4x+1` will have.

A

absolute maximum value

B

absolute minimum value

C

both absolute maximum and minimum values

D

None of these

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The absolute maximum and minimum values of functions can be found by their monotonic and asymptotic behaviour provided they exist. We may agree that finite limits values may be reagarded as absolute maximum or minimum. For instance the absolute maximum value of (1)/(1+x^(2)) is unity. It is attained at x=0 while absolute maximum value of the same functions is zero which is a limiting value of (xrarrooorxrarr-oo) The absolute minimum and maximum values of the function (x^(2)-x+1)/(x^(2)+x+1) is

The absolute maximum and minimum values of functions can be found by their monotonic and asymptotic behaviour provided they exist. We may agree that finite limits values may be reagarded as absolute maximum or minimum. For instance the absolute maximum value of (1)/(1+x^(2)) is unity. It is attained at x=0 while absolute maximum value of the same functions is zero which is a limiting value of (xrarrooorxrarr-oo) The absolute minimum value of the function (x-2)/(sqrt(x^(2)+1)) is

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ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. The absolute maximum and minimum values of functions can be found by t...

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  2. The least value of alpha in R for which 4ax^2+(1)/(x)ge1, for all xgt ...

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  3. The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is

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  4. Let f : R ->(0,oo) and g : R -> R be twice differentiable functions...

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  5. Let f:(0,oo) to vec R be given by f(x)=int(1/x)^x(e^(-(t+1/t))dt)/t , ...

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  6. The fuction f(x)=2|x|+|x+2|-||x+2|-2|x|| has a local minimum or a loca...

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  7. A rectangular sheet of fixed perimeter with sides having their lengths...

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  8. A vertical line passing through the point (h,0) intersects th ellipse ...

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  9. Let f,g and h be real-valued functions defined on the interval [0,1] b...

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  10. The total number of local maxima and local minima of the function f(x)...

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  11. If the function g:(-oo,oo)->(-pi/2,pi/2) is given by g(u)=2tan^-1(e^u)...

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  12. The second degree polynomial f(x), satisfying f(0)=o, f(1)=1,f'(x)gt...

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  13. If f(x)=x^3+bx^2+cx+d and 0<b^2<c, then

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  14. If f(x)=x^2+2b x+2c^2 and g(x)= -x^2-2c x+b^2 are such that min f(x...

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  15. The length of the longest interval in which the function 3sinx-4sin^3x...

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  16. If f(x)=e^(1-x) then f(x) is

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  17. The maximum value of (cosalpha(1))(cos alpha(2))...(cosalpha(n)), un...

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  18. If f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,, ""), (2- e^(x - 1),,"," 1 lt ...

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  19. If f(x) is a cubic polynomil which has local maximum at x=-1 . If f(2)...

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  20. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

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  21. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

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