Where is f(x) = x2e−x not increasing?

Question

Where is f(x) = x²e^-x not increasing?

Which of the following options is true?

(-inf , 0] ∪ [2 , inf)

(0 , 2)

[0 , 2]

(-inf,0) ∪ (2, inf)

Answer 1

It's not increasing anywhere its derivative is 0 or negative, i.e., df/dx <= 0. So take the derivative (using the multiplication rule). Next test the value of the derivative over the range of values provided. Remember () denotes an open interval (does not include the endpoints), whereas [] denotes a closed interval that does include the endpoints. When the symbols are mixed, e.g. (a,b], then a < x <= b.