then

A

f(x) attains its minimum at x=0

B

f(x) attains its maximum at x=0

C

f'(x) =0 at more than three points in `(-pi , pi)`

D

f(x) =0 at exactly three points in `(-pi, pi)`

Text Solution

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The correct Answer is:
B, C
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RESONANCE-APPLICATION OF DERIVATIVES-Exersise-3 Part I
  1. Let I RvecI R be defined as f(x)=|x|++x^2-1|dot The total number of po...

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  2. The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is 6 (b)...

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

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  4. A vertical line passing through the point (h,0) intersects the ell...

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  5. The function f(x)=2|x|+|x+2|=||x|2|-2|x|| has a local minimum or a loc...

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  6. Let f[0, 1] -> R (the set of all real numbers be a function.Suppose t...

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  7. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

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  8. line L:y=mx+3 meets y–axis at E(0, 3) and the are of the parabola y^(2...

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  9. Let a in R and let f: R to R be given by f(x) =x^(5) -5x+a. then

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  10. The slope of the tangent to the curve (y-x^5)^2=x(1+x^2)^2 at the poin...

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  11. A cylindrica container is to be made from certain solid material with ...

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  12. Let f,g:[-1,2]rarr RR be continuous functions which are twice differen...

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  13. Let f: R to (0 ,oo)" and " g :R to R be twice differentiable function...

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  14. Which of the following options is the only INCORRECT combination ?

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  15. Which of the following options is the only CORRECT combination

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  16. Which of the following options is the only CORRECT combination ?

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  17. If f:R->R is a twice differentiable function such that f''(x) > 0 for ...

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  18. If f:RR-> RR is a differentiable function such that f(x) > 2f(x) f...

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  19. then

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  20. For every twice differentiable function f: R->[-2,\ 2] with (f(0))^...

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