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

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(B) To find the intervals where the function $f(x) = x^4 - 4x^3 + 4x^2 + 40$ is monotonically decreasing, we first find its derivative $f'(x)$.$f'(x)

Vedclass · Accepted Answer

$1 < x < 2$

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(B) To find the intervals where the function $f(x) = x^4 - 4x^3 + 4x^2 + 40$ is monotonically decreasing, we first find its derivative $f'(x)$.$f'(x) = \frac{d}{dx}(x^4 - 4x^3 + 4x^2 + 40) = 4x^3 - 12x^2 + 8x$.Next, we factor the derivative:$f'(x) = 4x(x^2 - 3x + 2) = 4x(x - 1)(x - 2)$.$A$ function is monotonically decreasing when $f'(x) We analyze the sign of $f'(x) = 4x(x - 1)(x - 2)$ using the wavy curve method (sign scheme):- For $x - For $0 0$.- For $1 - For $x > 2$, $f'(x) > 0$.Thus, the function is monotonically decreasing for $x \in (-\infty, 0) \cup (1, 2)$.Comparing this with the given options, the correct interval is $1 < x < 2$.

For what values of $x$ is the function $f(x) = x^4 - 4x^3 + 4x^2 + 40$ monotonically decreasing?

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