Question:medium

Let \[ f(x)=x^3-\frac32x^2, \] which of the following is not correct?

Show Hint

To determine increasing or decreasing intervals, \[ \boxed{ \begin{aligned} f'(x)>0 &\Rightarrow \text{Increasing}, f'(x)<0 &\Rightarrow \text{Decreasing}. \end{aligned} } \] Always analyze the sign of the first derivative on each interval.
Updated On: Jul 14, 2026
  • In \((0,2)\), \(3x^2-3x-1=0\) has at least one solution.
  • \(f''(x)=0\) has a solution in \((0,2)\).
  • \(f(x)\) is increasing in \((-\infty,0)\) and \((1,\infty)\).
  • \(f(x)\) is decreasing in \((0,\infty)\).
Show Solution

The Correct Option is D

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