The function y = 2x^3 - 9x^2 + 12x - 6 is mon | vedclass

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(A) Given the function $f(x) = 2x^3 - 9x^2 + 12x - 6$. First,we find the derivative of the function with respect to $x$: $f'(x) = \frac{d}{dx}(2x^3 -

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$1 < x < 2$

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(A) Given the function $f(x) = 2x^3 - 9x^2 + 12x - 6$. First,we find the derivative of the function with respect to $x$: $f'(x) = \frac{d}{dx}(2x^3 - 9x^2 + 12x - 6) = 6x^2 - 18x + 12$. For the function to be monotonically decreasing,we must have $f'(x) $6x^2 - 18x + 12 Dividing the inequality by $6$,we get: $x^2 - 3x + 2 Factoring the quadratic expression: $(x - 1)(x - 2) This inequality holds when $x$ lies between the roots $1$ and $2$. Therefore,the function is monotonically decreasing for $1 < x < 2$.

The function $y = 2x^3 - 9x^2 + 12x - 6$ is monotonically decreasing when

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