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

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(B) Given function is $f(x) = x^3 - 6x^2 + 9x + 3$. To find the interval where the function is decreasing,we first find the derivative $f'(x)$. $f'(x)

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$(1, 3)$

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(B) Given function is $f(x) = x^3 - 6x^2 + 9x + 3$. To find the interval where the function is decreasing,we first find the derivative $f'(x)$. $f'(x) = \frac{d}{dx}(x^3 - 6x^2 + 9x + 3) = 3x^2 - 12x + 9$. Factorizing the derivative: $f'(x) = 3(x^2 - 4x + 3) = 3(x - 3)(x - 1)$. $A$ function is decreasing when $f'(x) So,$3(x - 3)(x - 1) This inequality holds when $x$ lies 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 in which interval does $x$ lie?

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