If f(x)=x^3-10x^2+200x-10,then | vedclass

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(C) Given function is $f(x) = x^3 - 10x^2 + 200x - 10$. To determine the intervals of increase or decrease,we find the derivative $f'(x)$. $f'(x) = \f

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$f(x)$ is increasing throughout the real line

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(C) Given function is $f(x) = x^3 - 10x^2 + 200x - 10$. To determine the intervals of increase or decrease,we find the derivative $f'(x)$. $f'(x) = \frac{d}{dx}(x^3 - 10x^2 + 200x - 10) = 3x^2 - 20x + 200$. To check the sign of $f'(x)$,we analyze the quadratic expression $3x^2 - 20x + 200$. The discriminant $D = b^2 - 4ac = (-20)^2 - 4(3)(200) = 400 - 2400 = -2000$. Since $D Since $f'(x) > 0$ for all $x \in \mathbb{R}$,the function $f(x)$ is strictly increasing throughout the real line.

If $f(x)=x^3-10x^2+200x-10$,then

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