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For all real values of x, the minimum v...

For all real values of x, the minimum value of `(1-x+x^2)/(1+x+x^2)` is
(A) 0
(B) 1
(C) 3
(D) `1/3`

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To find the minimum value of the function \( y = \frac{1 - x + x^2}{1 + x + x^2} \), we will follow these steps: ### Step 1: Differentiate the function We start by differentiating \( y \) with respect to \( x \). \[ y = \frac{1 - x + x^2}{1 + x + x^2} \] ...
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NCERT-APPLICATION OF DERIVATIVES-EXERCISE 6.5
  1. Show that of all the rectangles inscribed in a given fixed circle, th...

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  2. For all real values of x, the minimum value of (1-x+x^2)/(1+x+x^2) is...

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  3. The maximum value of [x(x-1)+1]^(1/3),0lt=xlt=1is(A) (1/3)^(1/3) (B) ...

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  4. Show that the semi-vertical angle of the cone of the maximum volume a...

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  5. A square piece of tin of side 18 cm is to be made into a box without ...

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  6. Find two positive numbers whose sum is 16 and the sum of whose cubes ...

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  7. Find two positive numbers x and y such that their sum is 35 and the ...

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  8. Find two positive numbers x and y such that x + y = 60and x y^3is max...

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  9. Find two numbers whose sum is 24 and whose product is as large as p...

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  10. Find the maximum and minimum values of x + sin2x on [0,2pi].

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  11. It is given that at x = 1, the function x^(4) - 62x^(2) + ax + 9 attai...

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  12. Find the maximum value of 2x^3-24 x+107 in the interval [1, 3]. Find ...

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  13. Find the maximum and minimum values, if any, of the following functio...

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  14. Find the maximum and minimum values, if any, of the following functio...

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  15. Find the local maxima and local minima, if any, of the following func...

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  16. Prove that the following functions do not have maxima or minima:(i) f...

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  17. Find the absolute maximum value and the absolute minimum value of the...

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  18. Find the maximum profit that a company can make, if the profit functi...

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  19. Find both the maximum value and minimum value of 3x^4-8x^3-48 x-25 ...

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  20. At what points in the interval [0,2pi], does the function sin 2x attai...

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