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The absolute maximum and minimum values ...

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

cot(sinx)

B

tan(logx)

C

`x^(2005)-x^(1947)+1`

D

`x^(2006)+x^(1947)+1`

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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-EXAMPLE
  1. Let f(x)=ax^(2)+c,a,b,c in R It is given |f(x)le1,AA|x|le1 Now , a...

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  2. The absolute maximum and minimum values of functions can be found by t...

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  3. The absolute maximum and minimum values of functions can be found by t...

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  4. Let f(x)={:{(max{t^(3)-t^(2)+t+1,0letlex}",",0lexle1),(min{3-t,1lttlex...

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  5. Let f(x)={:{(max{t^(3)-t^(2)+t+1,0letlex}",",0lexle1),(min{3-t,1lttlex...

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  6. Solve , x/3 - x/8 = 5/12

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  7. Find the value of x , (x - 3)/5 + (x - 4)/7 = 6 - (2x - 1)/(35)

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  8. Solve (2x +3)/3 = (7x + 45)/(15)

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  9. Solve , (x^2 - (x + 1)(x + 2))/(5x + 1) = 6

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  10. Prove that (7! - 5!)/(5!) = 41

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  11. If a function (continuos and twice differentiable) is always concave u...

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  12. Solve 3x + 2(x + 2) = 20 - (2x - 5)

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  13. If f(x)={(1)/(x)}andg(x)={x^(2)}, then the number of positive roots sa...

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  14. Match the Statements of Column I with values of Column II.

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  15. Match the Statements of Column I with values of Column II.

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  16. The set of all points where f(x) is increasing is (a,b)cup(c,oo). Find...

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  17. If f:[1,oo)rarrR:f(x) is monotonic and differentiable function and f(1...

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  18. Let f(x) be a cubic polynomial defined by f(x)=x^(3)/(3)+(a-3)x^(2)+...

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  19. If f(x)=max| 2 siny-x|, (where y in R), then find the minimum value o...

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  20. Let f(x)=sin^(-1)((2phi(x))/(1+phi^(2)(x))). Find the interval in whic...

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