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If f(x)=k x^3-9x^2+9x+3 monotonically in...

If `f(x)=k x^3-9x^2+9x+3` monotonically increasing in `R ,` then

A

`klt3`

B

`kle2`

C

`kge3`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
3
`f(x) = 3kx^(2)-18x+9=3 [kx^(2)-6x+3]ge0`
or `D=b^(2)-4aclt0,kgt0 i.e 36-12kle0`
or `kge3`
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CENGAGE PUBLICATION-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Exercise
  1. For all x in (0,1) (a) e^x<1+x (b) (log)e (1+x) < x (c) sin x > x (d) ...

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  2. If f(x)=x e^(x(x-1)) , then a) f(x) is increasing on [-1/2,1] b) decre...

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  3. If f(x)=k x^3-9x^2+9x+3 monotonically increasing in R , then

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  4. If the function f(x)=(Ksinx+2cosx)/(sinx+cosx) is strictly increasing ...

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  5. Let f: RvecR be a function such that f(x)=a x+3sinx+4cosxdot Then f(x)...

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  6. Which of the following statement is always true? If f(x) is increasing...

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  7. Let f: RvecR be a differentiable function for all values of x and has ...

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  8. Let f: Rvec be a differentiable function AAx in R . If the tangent dr...

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  9. Let f(x) be a function such that f^(prime)(x)=(log)(1/3)[(log)3(sinx+a...

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  10. If f(x)=x^3+4x^2+lambdax+1 is a monotonically decreasing function of x...

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  11. f(x)=|x loge x| monotonically decreases in (0,1/e) (b) (1/e ,1) (1,o...

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  12. The set of value(s) of a for which the function f(x)=(a x^3)/3+(a+2)x^...

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  13. The maximum value of the function f(x)=((1+x)^(0. 6))/(1+x^(0. 6)) in ...

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  14. Suppose that f is a polynomial of degree 3 and that f^(x)!=0 at any of...

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  15. A function g(x) is defined as g(x)=1/4f(2x^2-1)+1/2f(1-x^2) and f(x) i...

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  16. If varphi(x) is a polynomial function and varphi^(prime)(x)>varphi(x)A...

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  17. If f''(x) gt forall in R, f(3)=0 and g(x) =f(tan^(2)x-2tanx+4y)0ltxlt(...

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  18. If f(x)=x+sinx ,g(x)=e^(-x),u=sqrt(c+1)-sqrt(c) v=sqrt(c) -sqrt(c-1),(...

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  19. The number of solutions of the equation x^3+2x^2+6x+2cosx=0 where x in...

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  20. Let f(x)=cospix+10x+3x^2+x^3,-2lt=xlt=3. The absolute minimum value of...

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