Question 36: Let a function f whose derivative is \(f’\left( x \right) = x{(x + 1)^2}{(x – 2)^4}\) for all x ∈ R. The number of extreme points of the function f is:

We have

\(f’\left( x \right) = 0 \Leftrightarrow x{\left( {x + 1} \right)^2}{\left( {x – 2} \right)^2} = 0 \Leftrightarrow \left[\begin{array}{l}[\begin{array}{l}

x = 0\\

x = – 1\\

x = 2

\end{array} \right.\)

Variation table

Based on the variation table, we see that the function has a minimum at x = 0. So the function has an extreme.

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