Question 36: Know that the function f(x) is determined on R and has the derivative f'(x) = (x – 1)x2(x + 1)3(x + 2)4. How many extreme points does the function have?

f'(x) = (x – 1)x^{2}(x + 1)^{3}(x + 2)^{4}

We see that the equation f'(x) = 0 has 2 simple roots of 1; -1 and 2 double roots are 0; -2

Hence, the maximum score is 2.

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