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Let f(x)= {{:(1+ sin x, x lt 0 ),(x^2...

Let `f(x)= {{:(1+ sin x, x lt 0 ),(x^2-x+1, x ge 0 ):}`

A

f has a local maximum at x = 0

B

f has a local minimum at x = 0

C

f is increasing evrywhere

D

f is decreasing everwhere

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The correct Answer is:
A
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FIITJEE-APPLICATION OF DERIVATIVE-SOLVED PROBLEMS (OBJECTIVE)
  1. Find critical points of f(x) =max (sinx cosx) AA , X in (0, 2pi).

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  2. A function f(x) =(x^(2) -3x +2)/(x^(2)+ 2x -3) is

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  3. Let f(x)= {{:(1+ sin x, x lt 0 ),(x^2-x+1, x ge 0 ):}

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  4. The least natural number a for which x+ax^(-2)gt2,AAx in (0,oo) is -

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  5. The number of solutions of the equation x^3 +2 x^2 +5 x + 2 cos x = 0 ...

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  6. If N is any four digit number say x1, x2, x3, x4, then the maximum val...

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  7. Let{:{(|x-1|+a, x lt 1), (2x+3, x ge 1):} if f(x) has a local minima ...

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  8. For y=f(x)=overset(x)underset(0)int 2|t|dt, the tangent lines parallel...

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  9. f(x) is cubic polynomial which has local maximum at x = -1. If f(2) = ...

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  10. The inequality x^(2)-3x gt tan^(-1) x is ture in

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  11. If f(x)=(sin^(2)x-1)^(n) (2+cos^(2)x), then x = pi/2 is a point of

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  12. Let f(x)=int(0)^(x)e^(t)(t-1)(t-2)dt. Then, f decreases in the interva...

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  13. Range of the function f(x) = (x-1)^(5)/(x^(5)-1) is

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  14. Range of the function f(x)= x^(2)-6x+5/x^(2)-5x+6 is

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  15. Range of the function f(x)= x cos( 1/x), xgt1

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  16. If both the critical points of f(x) = ax^(3)+bx^(2) +cx +d are -ve the...

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  17. The least number of imaginary roots of f(x) = ax^(6)+bx^(4)+cx^(2)+dx ...

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  18. Statement -1: f(x) = x^(3)-3x+1 =0 has one root in the interval [-2,2]...

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  19. If the equation x^(2)-3x+|3x-a|le0 is to be satisfied by atleast one x...

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  20. If f(x) is differentiable and strictly increasing function, then the v...

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