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If (f(x)-1) (x ^(2) + x+1)^(2) -(f (x)+1...

If `(f(x)-1) (x ^(2) + x+1)^(2) -(f (x)+1) (x^(4) +x ^(2) +1) =0`
`AA x in R -{0}and f (x) ne pm 1,` then which of the following statement (s) is/are correct ?

A

`|f (x)ge 2 AA x in R -{0}`

B

`f (x)` has a local maximum at `x=-1`

C

`f (x)` has a local minimum at `x=1`

D

`int _(-pi) ^(pi) (cos x ) f(x) dx =0`

Text Solution

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The correct Answer is:
A, B, C, D
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VK JAISWAL-APPLICATION OF DERIVATIVES -EXERCISE (ONE OR MORE THAN ANSWER IS/ARE CORRECT )
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  9. d (x) = int (0) ^(x) e ^(t ^(3)) (t ^(2) -1) (t+1) ^(2011) at (x gt 0)...

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  14. Which of the following is/are true for the function f(x)= int (0) ^(x)...

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  15. Let F (x) = (f (x ))^(2) + (f' (x ))^(2), F (0) =6, whtere f (x) is a ...

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  16. Let f(x) = {{:( x^(3) + x^(2) - 10 x ,, -1 le x lt 0) , (sin x ,, 0 le...

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  17. Minimum distnace between the curves y ^(2) =x-1and x ^(2) =x-1 and x ^...

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  18. For the equation (e^-x)/(x+1) which of the following statement(s) is/a...

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  19. If y = m x +5 is a tangent to the curve x ^(3) y ^(3) = ax ^(3) +by^(...

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  20. If (f(x)-1) (x ^(2) + x+1)^(2) -(f (x)+1) (x^(4) +x ^(2) +1) =0 AA x...

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