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2x^(3) - 6x + 5 is an increasing functio...

`2x^(3) - 6x + 5` is an increasing function, if

A

` 0 lt x lt 1`

B

`-1 lt x lt 1`

C

` x lt -1 or x gt 1`

D

`-1 lt x lt -(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)` is an increasing function , if `f(x) gt 0`
Let `f(x) = 2x^(3) - 6x + 5`
On differenting , w.r.t .x, we get
`f(x) = 6x^(2) - 6`
Since f(x) is increasing function.
`rArr " " 6x^(2) - 6 gt 0`
` rArr (x - 1) (x+1) gt 0`
` rArr " " x gt 1 or x lt -1 `
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 11 -PAPER 2 (MATHEMATICS )
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  3. (d)/(dx) int(2)^(x^(2)) (t -1) dt is equal to

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  4. int(0)^(pi//2) (cos theta)/(sqrt(4-sin^(2)theta))d theta is equal to

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  5. int x{f(x)^(2) g''(x^(2))-f''(x^(2)) g(x^(2))}dx is equal to

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  6. lim(x to (pi)/(6)) [(3sinx - sqrt(3)cos x)/(6x -pi)] is equal to

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  7. Let f(x) = {{:(,x +1,"where " x lt 2),(,2x -1,"where" x ge 2):} then ...

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  8. Show that the area' bounded by the curve y = ce^x (c> 0), the x-axis a...

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  9. Let inputs of p and q be 1 and 0 respectively in electric circuit ...

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  10. Digital circuit shown beow represents Boolea expression as

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  11. If a^(2),b^(2),c^(2) are in AP, then which of the following is also an...

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  12. Geometric mean of 7,7^(2), 7^(3) ,……….7^(n) is

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  13. The sum of the distance of a point (2,-3) form the foci of an ell...

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  14. A={1,2},B={{1},{2}},C={{1,2}}. Then, which of the following relation i...

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  15. R is a relation on N given by R={(x,y):4x+3y=20}. Which of the follo...

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  16. At what point on the curve x^(3) - 8a^(2) y= 0 the slope of the nor...

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  17. The radius of a cylinder is increasing at the rate of 3ms^(-1) and its...

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  18. The inverse matrix of A=[(0,1,2),(1,2,3),(3,1,1)] is

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  19. If the x-coordinate of a point P on the jon of Q(2,2,1) and R(5,1,-2) ...

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