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Question

Show that the function f given by f(x)=x33x2+4x,xR is strictly increasing.

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Solution

f(x)=x33x2+4x
f(x)=ddx(x33x2+4x)
=3x26x+4
=3x26x+3+1
=3(x2x+1)+1
=3(x1)2+1
As square is a positive number.
The value of f(x) will always be positive for real number.

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