The function f(x) = 2x^3 - 9x^2 + 12x + 29 is | vedclass

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Question

(D) function $f(x)$ is monotonically decreasing when its derivative $f'(x) < 0$.Given $f(x) = 2x^3 - 9x^2 + 12x + 29$.First,find the derivative $f'(x)

Vedclass · Accepted Answer

$1 < x < 2$

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(D) function $f(x)$ is monotonically decreasing when its derivative $f'(x) Given $f(x) = 2x^3 - 9x^2 + 12x + 29$.First,find the derivative $f'(x)$:$f'(x) = \frac{d}{dx}(2x^3 - 9x^2 + 12x + 29) = 6x^2 - 18x + 12$.Set $f'(x) $6x^2 - 18x + 12 Divide the entire inequality by $6$:$x^2 - 3x + 2 Factor the quadratic expression:$(x - 1)(x - 2) For the product of two factors to be negative,the value of $x$ must lie between the roots $1$ and $2$.Therefore,the function is monotonically decreasing when $1 < x < 2$.

The function $f(x) = 2x^3 - 9x^2 + 12x + 29$ is monotonically decreasing when:

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