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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 \( f(x) = \frac{1 - x + x^2}{1 + x + x^2} \), we will follow these steps: ### Step 1: Find the first derivative of the function We will use the quotient rule for differentiation. The quotient rule states that if we have a function \( \frac{u}{v} \), then its derivative is given by: \[ f'(x) = \frac{u'v - uv'}{v^2} \] ...
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NCERT ENGLISH-APPLICATION OF DERIVATIVES-EXERCISE 6.5
  1. Show that of all the rectangles inscribed in a given fixed circle, ...

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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 a right circular cone of ma...

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  5. A square piece of tin of side 18 cm is to be made into a box withou...

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

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

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  8. Find two positive numbers x and y such that x+y=60 and x y^3 is 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 f(x)=x+sin2x in the interval...

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  11. It is given that at x=1 , the function x^4-62 x^2+a x+9 attains its ma...

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

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  13. Find the maximum and minimum values , if any , of the function f given...

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

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  15. Find the points of local maxima or local minima, if any, of the fol...

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

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

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

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  19. Find the maximum value and the minimum value and the minimum value of ...

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

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