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Consider f (x)= sin ^(5) x-1, x in [0, (...

Consider `f (x)= sin ^(5) x-1, x in [0, (pi)/(2)],` which of the following is/are correct ?

A

f is strictly decreasing in `[0, (pi)/(4)]`

B

f is strictly increasing in `[(pi)/(4),(pi)/(2)]`

C

There exist a numbe 'c' in `(0,(pi)/(2))` such that `f (c ) =0`

D

The equation `f (x)=0` has only two roots in` [0,(pi)/(2)]`

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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  2. Let m and n bwe positive integers and x,y gt 0 and x+y =k, where k is ...

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  3. Determine the equation of straight line which is tangent at one point ...

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  4. A curve is such that the ratio of the subnomal at any point to the sum...

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  5. Number of A parabola of the form y= ax^2 +bx+c with a>0 intersectio...

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  6. Find the gradient of the line passing through the point (2,8) and touc...

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  7. The equation x + cos x = a has exactly one positive root. Complete set...

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  8. Given that f (x) is a non-constant linear function. Then the curves :

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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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  10. Let f(x)=sinx+a x+bdot Then which of the following is/are true? f(x)=0...

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  11. Which of the following graphs represent function whose derivatives hav...

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  12. Consider f (x)= sin ^(5) x-1, x in [0, (pi)/(2)], which of the followi...

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  13. Let f (x)= [{:(x ^(2alpha+1)ln x ,,, x gt0),(0 ,,, x =0):} If f (x) sa...

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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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