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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.

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

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

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

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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.

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.

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