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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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 incr

Vedclass · Accepted Answer

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

Vedclass · Answer

(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?

Similar Questions

The length of the longest interval in which the function $f(x) = 3\sin x - 4\sin^3 x$ is increasing is:

If $f(x) = \frac{\log x}{x}$ $(x > 0)$,then it is increasing in

The function $f(x) = x + \cos x$ is

$F(x) = \log |\sin x|$,where $x \in (0, \pi)$,is strictly increasing on

If $f(x) = \sin x - \cos x,$ the function is decreasing in the interval $0 \le x \le 2\pi$ for which of the following?

Vedclass Test Series

Exam Paper Generator

Online Exam Module