If f(x) = x^3 - 6x^2 + 9x + 3 is a decreasing | vedclass

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(B) Given function: $f(x) = x^3 - 6x^2 + 9x + 3$. For a function to be decreasing,its derivative must be less than zero,i.e.,$f'(x) < 0$. First,find t

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$(1, 3)$

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(B) Given function: $f(x) = x^3 - 6x^2 + 9x + 3$. For a function to be decreasing,its derivative must be less than zero,i.e.,$f'(x) First,find the derivative: $f'(x) = \frac{d}{dx}(x^3 - 6x^2 + 9x + 3) = 3x^2 - 12x + 9$. Set the inequality: $3x^2 - 12x + 9 Divide the entire inequality by $3$: $x^2 - 4x + 3 Factorize the quadratic expression: $(x - 3)(x - 1) To satisfy this inequality,$x$ must lie between the roots $1$ and $3$. Therefore,$x \in (1, 3)$.

If $f(x) = x^3 - 6x^2 + 9x + 3$ is a decreasing function,then $x$ lies in:

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