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Statement 1: For all a ,b in R , the fu...

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.

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

Prove that for all a,b in the function f(X) =3x^(4)-4x^(3)+6x^(2)+ax+b has exactly one extremium.

The function f(x)=2+4x^(2)+6x^(4)+8x^(6) has

The function f(x)=x^(6)-x-1 cuts the x - axis

For what values of x the function f(x)=x^(4)-4x^(3)+4x^(2)+40 is monotonic decreasing?

The function f(x)=2x^(3)-3(a+b)x^(2)+6abx has a local maximum at x=a , if

For what values of x the function f(x)=x^(4)-4x^(3)+40 si monotonic decreassing?

Statement I :The function f(x)=(x^(3)+3x-4)(x^(2)+4x-5) has local extremum at x=1. Statement II :f(x) is continuos and differentiable and f'(1)=0.

Discuss the function f(x)=x^(6)-3x^(4)+3x^(2)-5, and plot the graph.

BANSAL-APPLICATION OF DERIVATIVE-All Questions
  1. The set of values of p for which the points of extremum of the functio...

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  2. The difference between the greatest and the least value of f(x)=cos...

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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. If the equation x^3-12 x+a=0 has exactly one real root, then range ...

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  5. The set of values of p for which the points of extremum of the functio...

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  6. Let S be the set of all x such that x^4-10 x^2+9lt=0 . The maximum val...

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  7. The lower corner of a leaf in a book is folded over so as to reach the...

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  8. P is a point on positive x-axis, Q is a point on the positive y-...

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  9. Consider the cubic f(x)=8x^3+4a x^2+2b x+a where a , b\ in Rdot For...

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  10. For b=1,\ if y=f(x)=8x^3+4x^2+2bx+1 is non monotonic then the sum o...

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  11. If the sum of the base 2 logarithms of the roots of the cubic f(x)= ...

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  12. Consider the function f(x)=x^(30)dot(lnx)^20 for x >0 If f is continu...

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  13. Maximum value of f(x)=(lnx)^20.x^30 occurs at x=-2/3 (b) x=1 x=e^(-2...

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  14. Consider the function f(x)a n d\ g(x) such that f(x)=(x^3)/2+1-x\ i...

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  15. consider a function f(x) Minimum distance between the functions f(x)...

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  16. Let f(x) be a real valued continuous function on R defined as f(x)=...

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  17. Consider the function f(x) and g(x) such that f(x)=x^2/2+1-x+intg(x)dx...

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  18. let f(x)=(x^2-1)^n (x^2+x-1) then f(x) has local minimum at x=1 when

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  19. An extremum value of y=int0^x(t-1)(t-2)dt is : 5/6 (b) 2/3 (c) 1 ...

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  20. The function f(x)=int(-1)^x t(e^t-1)(t-1)(t-2)^3(t-3)^5dt has a local ...

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