Q56 / 150 · MHT CET 2024 (09 May Shift 2) · Mathematics
The function $\mathrm{f}(x)=2 x^3-6 x+5$ is an increasing function, if
- A$0 \lt x \lt 1$
- B$-1 \lt x \lt 1$
- Correct answerC$x \lt -1$ or $x\gt1$
- D$-1 \lt x \lt -\frac{1}{2}$
Solution
$\begin{aligned}
& f(x)=2 x^3-6 x+5 \\
\therefore \quad & f^{\prime}(x)=6 x^2-6
\end{aligned}$
For $\mathrm{f}(x)$ to be increasing, $\mathrm{f}^{\prime}(x)\gt0$ $\begin{aligned} & \Rightarrow 6 x^2-6\gt0 \Rightarrow(x-1)(x+1)\gt0 \\ & \Rightarrow x\gt1 \text { or } x \lt -1 \end{aligned}$
For $\mathrm{f}(x)$ to be increasing, $\mathrm{f}^{\prime}(x)\gt0$ $\begin{aligned} & \Rightarrow 6 x^2-6\gt0 \Rightarrow(x-1)(x+1)\gt0 \\ & \Rightarrow x\gt1 \text { or } x \lt -1 \end{aligned}$
Hence, the correct answer is option: 'C'.