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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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A DAS GUPTA-Some New Pattern Problems-Exercise
  1. Let p(x) be a polynomial of degree 4 having extremum at x = 1,2 and l...

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

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  3. If the function f(x)=x^(3)+e^(x//2)andg(x)=f^(-1)(x), then the value ...

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  4. Let f:R rarr R be a continous function which satisfies f(x)= int (0)^(...

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  5. The smallest value of k for which both the roots of the equation x^2-8...

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  6. Let w be the complex number cos(2pi)/3 + sin(2pi)/3. Then the number o...

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  7. Let sk, k=1,2,3,…,100 denote the sum of the infinite geometric series ...

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  8. The number of all possible values of theta, where 0 lt theta lt pi, f...

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  9. The number of values of theta in the interval (-(pi)/(2), (pi)/(2)) su...

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  10. The maximum value of the expression 1/(sin^2theta+3sinthetacostheta+5c...

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  11. The line 2x + y = 1 is tangent to the hyperbola x^2/a^2-y^2/b^2=1. I...

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  12. If vec a and vec b are vectors in space given by vec a= (hat i - 2vec ...

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  13. Lines (x-1)/2 = (y-2)/3 = (z-3)/4 and (x-2)/3 = (y-3)/4 = (z-4)/5 lie ...

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  14. Let f be a real-valued differentiable function on R (the set of ...

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  15. For any real number x, let [x]= largest integer less than or equalto x...

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  16. Le a1, a2, a3, ,a(11) be real numbers satisfying a2=15 , 27-2a2>0a n ...

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  17. Two parallel chords of a circle of radius 2 are at a distance sqrt3 + ...

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  18. Consider a triangle ABC and let a , b , and c denote the lengths of t...

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  19. Let K be a positive real number and A=[2k-1 2sqrt(k)2sqrt(k)2sqrt(k)1-...

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

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