Question

You are given that
f(x) =1+ax+ax2
f′(x) =−(x+2)ax3
f′′(x) =(2x+6)ax4

and the constant a>0.

Write down all intervals on which the function is increasing, decreasing, concave up or concave down.

(Enter using notation (a, b). Use a comma to separate multiple intervals; e.g. (a, b), (c, d). Type inf and -inf to denote ∞ and −∞ respectively.)

increasing:
- sin responder


decreasing:
- sin responder


concave up:
- sin responder


concave down:
- sin responder

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F. (10) (4 puntos posibles)

Sketch the graph of f(x)=1+ax+ax2 (same function as above) on −∞<x<∞ showing the horizontal and vertical asymptotes. While the sketch need not be to scale, please make sure the x− coordinate of all critical point(s) and inflection point(s) are accurate.