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Statement 1: For all `a ,b in R ,` the function `f(x)=3x^4-4x^3+6x^2+a x+b` has exactly one extremum. Statement 2: If a cubic function is monotonic, then its graph cuts the x-axis only one.

A

No extremum

B

Exactly one extremum

C

Exactly two extremum

D

Three extremum

Text Solution

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The correct Answer is:
B
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AAKASH INSTITUTE ENGLISH-APPLICATION OF DERIVATIVES-Assignment SECTION-A (Competition Level Questions)
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  2. A curve is represented by the equations x=sec^2ta n dy=cott , where t ...

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  3. Statement 1: For all a ,b in R , the function f(x)=3x^4-4x^3+6x^2+a x...

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  4. Maximum area of a reactangle which can be inscribed in a circle of a...

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  5. If atmosphere pressure at a height of h units is given by the function...

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  6. The radius of cylinder of maximum volumne which can be inscribed in a...

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  7. Let f(x)={{:(-|x-2|, ,x le 3 ),(x^(2)-2x-4,, x gt 3 ):} Then the n...

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  8. The curve y-e^(xy)+x=0 has a vertical tangent at the point:

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  9. Consider the function f(x)=xcosx-sinxdot Then identify the statement w...

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  10. If x=2t-3t^(2) and y=6t^(3) then (dy)/(dx) at point (-1,6) is

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  11. For the cubic function f(x)=2x^3+9x^2+12 x+1, which one of the followi...

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  12. The function f is defined by f(x)=x^(p)(x-1)^(q)"for all "x inR, where...

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  13. Let h be a twice continuosly differentiable positive function on an op...

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  14. The least area of the circle circumscribing and right triangle of area...

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  15. If f(x)=x(1-x)^(3) then which of following is true ?

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  16. Discuss monotonocityt of y =f(x) which is given by x=(1)/(1+t^(2))and ...

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  17. The point on the curve y^(2)=x where tangent makes 45^(@) angle with x...

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  18. The radius of a right circular cylinder increases at a constant rate. ...

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  19. Two sides of a triangle are to have lengths 'a'cm & 'b'cm. If the tria...

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  20. The cost function at American Gadget is C(x)=x^(3)-6x^(2)+15x (x is i...

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