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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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CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Let a in R and let f: R be given by f(x)=x^5-5x+a , then (a) f(x) ...

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  2. Match the statement/expressions in Column I with the open intervals in...

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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. f(x) is cubic polynomial with f(x)=18 and f(1)=-1 . Also f(x) has loca...

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  5. f(x)={(c^x ,,0lexle1),(2-c^(x-1) , ,1ltxlt=2),( x-c ,,2ltxlt=3):}, and...

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  6. A rectangular sheet of fixed perimeter with sides having their lengths...

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  7. The function f(x)=x/2+2/x has a local minimum at (a) x=2 (b) x=-2 (c...

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  8. Statement 1: Let f(x)=5-4(x-2)^(2/3)dot Then at x=2, the function f...

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  9. Let f: RvecR be differentiable and strictly increasing function throug...

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  10. The function defined by f(x)=(x+2)e^(-x) is decreasing for all x decr...

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  11. Statement 1: If f(x) is an odd function, then f^(prime)(x) is an even ...

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  12. Prove that f(x)=a^x, 0<a<1, is decreasing in R.

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  13. Assertion Consider the following statements in S and R S: Both sinx a...

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  14. Statement 1: The function f(x)=x In x is increasing in (1/e ,oo) Stat...

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  15. Statement 1: f(x)=|x-1|+|x-2|+|x-3| has point of minima at x=3. State...

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  16. Find the point on the curve 4x^2 + a2y^2 = 4a^2, 4 < a^2 < 8 that is f...

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  17. Statement 1: For all a ,b in R , the function f(x)=3x^4-4x^3+6x^2+a x...

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  18. Statement 1: f(x)=(x^3)/3+(a x^2)/2 + x+5 has positive point of maxima...

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  19. If a function f(x) has f^(prime)(a)=0 and f^(primeprime)(a)=0, then (...

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  20. The minimum value of 2^((x^2-3)^3+27) is (a) 2^(27) (b) 2 (c) 1 (d...

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