State the nature of each turning point for :?

Question

y = [x^4] [e^-x]

Answer 1

the first derivative of this expression wrt x is:

dy/dx = (4-x).x^3.e^-x which goes to zero indicating turning points, at x=0 and at x = 4

Simple inspection of the form of the curve of this function quickly shows that these turning points are respectively a minimum (at x=0) and a maximum (at x=4).

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