The function f(x) = 2x^3 - 9x^2 + 12x + 2 is | vedclass

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(A) Given function: $f(x) = 2x^3 - 9x^2 + 12x + 2$. Find the derivative: $f'(x) = 6x^2 - 18x + 12$. For the function to be decreasing,we must have $f'

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$1 < x < 2$

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(A) Given function: $f(x) = 2x^3 - 9x^2 + 12x + 2$. Find the derivative: $f'(x) = 6x^2 - 18x + 12$. For the function to be decreasing,we must have $f'(x) $6x^2 - 18x + 12 Divide by $6$: $x^2 - 3x + 2 Factor the quadratic expression: $(x - 1)(x - 2) Using the sign scheme for the inequality,the expression is negative between the roots $x = 1$ and $x = 2$. Thus,the function is decreasing in the interval $(1, 2)$.

The function $f(x) = 2x^3 - 9x^2 + 12x + 2$ is decreasing in

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