Observe the following statements A: f(x)=2x^3 | vedclass

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(A) For the function $f(x) = 2x^3 - 9x^2 + 12x - 3$,the derivative is $f'(x) = 6x^2 - 18x + 12 = 6(x^2 - 3x + 2) = 6(x-1)(x-2)$.For $f(x)$ to be incre

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Both $A$ and $R$ are true,and $R$ is not the correct reason for $A$

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(A) For the function $f(x) = 2x^3 - 9x^2 + 12x - 3$,the derivative is $f'(x) = 6x^2 - 18x + 12 = 6(x^2 - 3x + 2) = 6(x-1)(x-2)$.For $f(x)$ to be increasing,we require $f'(x) > 0$,which implies $6(x-1)(x-2) > 0$. This inequality holds when $x  2$. Thus,$f(x)$ is increasing outside the interval $(1,2)$. Hence,statement $A$ is true.For statement $R$,we check the condition $f'(x) Since statement $A$ describes the increasing behavior and statement $R$ describes the decreasing behavior,$R$ is not the reason for $A$. Therefore,both $A$ and $R$ are true,but $R$ is not the correct explanation for $A$.

Observe the following statements $A$: $f(x)=2x^3-9x^2+12x-3$ is increasing outside the interval $(1,2)$. $R$: $f'(x) < 0$ for $x \in (1,2)$. Then,which of the following is true?

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