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The condition f(x)=x^3 + px^2 + qx +r...

The condition
`f(x)=x^3 + px^2 + qx +r ( x in R)` to have no extreme value is

A

`p^2 lt 3q`

B

`2p^2 lt q`

C

`p^ 2 lt q/4`

D

`p^2 gt 3q`

Text Solution

Verified by Experts

The correct Answer is:
A
If `f(x)=x^3+px^2+qx+r` hasm no exterme value, then
`f(x) ne "for any" x in R`
`rArr 3x^2+2px + q =0 ` has no real root
` rArr 4 p^2-12 q lt 0 rArr p^2 lt 3q`
In order to determine extreme values of a function we may use the following algorithum .
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OBJECTIVE RD SHARMA ENGLISH-MAXIMA AND MINIMA -Chapter Test
  1. The condition f(x)=x^3 + px^2 + qx +r ( x in R) to have no extreme ...

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  2. The maximum value of ((1)/(x))^(2x^(2)) is

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  3. If a x^2+b/xgeqc for all positive x where a >0 and b >0, show that 27 ...

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  4. The greatest value of the funxtion f(x)=xe^(-x) " in " [0,oo] is

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  5. Let f(x)=x^3-6x^2+12x-3 . Then at x=2 f(x) has

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  6. In the right triangle BAC, angle A=pi/2 and a+b=8. The area of the tr...

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  7. The range of values of a for which the function f(x)=(a^2-7a+12)cosx...

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  8. If the function f(x) = (2a-3)(x+2 sin3)+(a-1)(sin^4x+cos^4x)+log 2...

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  9. The function y=(ax+b)/(x-1)(x-4) has turning point at P(2,-1) Then fin...

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  10. Find the least value of the expressions 2log(10)x-log(x)0.01, where xg...

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  11. The maximum value of the function f(x) given by f(x)=x(x-1)^2,0ltxlt...

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  12. The least value of a for which the equation 4/(sinx)+1/(1-sinx)=a has ...

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  13. The minimum value of f(x)=e^((x^4-x^3+x^2)) is

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  14. Let f(x)=a/x+x^2dot If it has a maximum at x=-3, then find the value o...

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  15. Find the maximum value of 4sin^(2)x+3cos^(2)x+sin""(x)/(2)+cos""(x)/(2...

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  16. The least value of the f(x) given by f(x)=tan^(-1)x-1/2 logex " in t...

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  17. The slope of the tangent to the curve y=e^x cosx is minimum at x= a,0 ...

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  18. The value of a for which the function f(x)={{:(tan^(-1)a -3x^2" , " ...

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  19. The minimum value of 27^(cos3x)81^(sin3x) is

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  20. If f(x)=(x^2-1)/(x^2+1) . For every real number x , then the minimum v...

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  21. f(x) = |x|+|x-1| +|x-2|, then which one of the following is not correc...

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