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Let f be a function defined on R (the se...

Let `f` be a function defined on `R` (the set of all real numbers) such that `f^(prime)(x)=2010(x-2009)(x-2010)^2(x-2011)^3(x-2012)^4,` for all `x in Rdot` If `g` is a function defined on `R` with values in the interval `(0,oo)` such that `f(x)=ln(g(x)),` for all `x in R ,` then the number of point is `R` at which `g` has a local maximum is ___

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ARIHANT MATHS ENGLISH-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If the function g:(-oo,oo)->(-pi/2,pi/2) is given by g(u)=2tan^-1(e^u)...

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

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

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

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

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

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

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

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

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  11. about to only mathematics

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  12. Find a point on the curve x^2 + 2y^2 = 6, whose distance from the li...

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  13. Let I RvecI R be defined as f(x)=|x|++x^2-1|dot The total number of po...

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  14. Let p(x) be a real polynomial of least degree which has a local maximu...

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  15. Let f be a function defined on R (the set of all real numbers) such th...

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  16. The maximum value of the expression (1)/(sin ^(2) theta + 3 sin thet...

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  17. The maximum value of the function f(x)=2x^3-15 x^2+36 x-48 on the set ...

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  18. A wire of length 2 units is cut into two parts which are bent respecti...

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  19. If x =-1 and x=2 ar extreme points of f(x) =alpha log|x|+betax^(2)+x ,...

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  20. Let a , b in R be such that the function f given byf(X) = ln |x|+bx^(2...

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