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Find the polynomial f(x) of degree 6, wh...

Find the polynomial f(x) of degree 6, which satisfies `underset(x to 0) ("Limit") (1 + (f(x))/(3))^(1//x) = e^(2)` and has local maximum at x = 1 and local minimum at x = 0 & 2.

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A DAS GUPTA-Maxima and Minima-EXERCISE
  1. Find the polynomial f(x) of degree 6, which satisfies underset(x to 0...

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  2. Find the maxima and minimum value of the function y = 40/(3x^(4)+ 8x^(...

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  3. f (x) =2x -tan ^(-1) x - ln (x+ sqrt(1+ x ^(2)))

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  4. Show that f(x) = sqrt(e^(x^(2))-1) has its extremum at x = 0. Also me...

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  5. Using examples, prove that the conditiondy/dx = 0 is neither a necessa...

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  6. Let f(x) = x ^3 - 12x. Prove that the equation x^3 - 12x - k = 0 has a...

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  7. If y=a log x +bx^(2)+x has its exteme values at x=-1 and x=2, then fin...

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  8. If y=(a x-b)/((x-1)(x-4)) has a turning point P(2,-1), find the value ...

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  9. Find the shortest distance of the point (0, c) from the parabola y=x^...

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  10. Find the coordinates of a point on the parabola y=x^2+7x+2 which is cl...

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  11. Given an interior point A on the axis of the parabola y ^2 = 2px, (p >...

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  12. Find the coordinates of the point on the curve y=x/(1+x^2) where the t...

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  13. The parametric equations of the curve are x=2t(t^2+3)-3t^2, y=2t(t^2+3...

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  14. A function is defined parametrically as follows :x=t^5-5t^3-20 t+7y=4t...

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  15. Let (h , k) be a fixed point, where h >0,k > 0. A straight line passin...

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  16. A 12-cm-long wire is bent to form a triangle with one of the angles as...

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  17. The largest area of a rectangle which has one side on the x-axis and t...

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  18. Three sides of a trapezium are each equal to k cm. Find the greatest p...

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  19. A statue 4 meters high sits on a column 5.6 meters high . How far f...

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  20. A wire of length l is cut into two parts. One part is bent into a circ...

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  21. A point P is given on the circumference of a circle of radius rdot Cho...

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