For what values of x is the function f(x) = x | vedclass

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(A) Given the function $f(x) = x^3 - 3x^2 - 9x + 22$. To find the interval where the function is strictly decreasing,we calculate the derivative $f'(x

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$-1 < x < 3$

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(A) Given the function $f(x) = x^3 - 3x^2 - 9x + 22$. To find the interval where the function is strictly decreasing,we calculate the derivative $f'(x)$. $f'(x) = \frac{d}{dx}(x^3 - 3x^2 - 9x + 22) = 3x^2 - 6x - 9$. For the function to be strictly decreasing,$f'(x) $3x^2 - 6x - 9 Dividing by $3$,we get $x^2 - 2x - 3 Factoring the quadratic expression: $(x - 3)(x + 1) The roots of the equation $(x - 3)(x + 1) = 0$ are $x = 3$ and $x = -1$. Testing the intervals $(-\infty, -1)$,$(-1, 3)$,and $(3, \infty)$,we find that the expression is negative in the interval $(-1, 3)$. Therefore,the function is strictly decreasing for $-1 < x < 3$.

For what values of $x$ is the function $f(x) = x^3 - 3x^2 - 9x + 22$ strictly decreasing?

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