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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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VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS 2-JEE Advanced (Archive)
  1. Let p(x) be a real polynomial of least degree which has a local maximu...

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  2. The number of distinct real roots of x^(4) - 4x^(3) + 12 x^(2) + x - ...

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

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

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

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  6. A cylindrical container is to be made from certain solid material with...

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  7. The slope of the tangent to the curve (y-x^5)^2=x(1+x^2)^2 at the poin...

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  8. Let C be the curve y^(3) - 3xy + 2 =0. If H is the set of points on th...

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  9. Let fa n dg be differentiable on [0,1] such that f(0)=2,g(0),f(1)=6a n...

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  10. if |f(x1)-f(x2)|<=(x1-x2)^2Find the equation of tangent to the curve y...

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  11. The curve y=a x^3+b x^2+c x+5 touches the x-axis at P(-2,0) and cuts t...

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  12. Tangent at a point P(1) [other than (0,0)] on the curve y=x^(3) meets ...

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  13. Find the equation of the normal to the curve y=(1+x)^y+sin^(-1)(s i...

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  14. Find the equation of tangents to the curve y=cos(x+y),-2pilt=xlt=2pi t...

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  15. The set of all x for which log(1+ x) le x is equal to …… .

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  16. The function y=2x^2-log(x) is monotonically increasing for values of x...

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  17. Prove that for x in [0, (pi)/(2)], sin x + 2x ge (3x(x + 1))/(pi).

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  18. Using the relation 2(1−cosx)<x^2 ,x=0 or prove that sin(tanx)≥x,∀ϵ[0,...

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  19. Let -1leple1, show that the equation 4x^(3)-3x-p=0 has a unique root i...

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  20. Let f(x)={{:(xe^(ax)",", x le0),(x+ax^2-x^3",",x gt 0):} where a is po...

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