Fine the open intervals on which the graph of f(x) = -x^5+20x^4-130x^3+280x^2-245x+724 is concave upward and those on which it is concave downward.
a. Concave upward (1,4) and (7, ∞); concave downward (-∞, 1) and (4,7)
b. Concave upward (-∞, 0) and (3,6); concave downward (0,3) and (6, ∞)
c. Concave upward (-∞, 1) and (4, 7); concave downward (1,4) and (7, ∞)
d. None of These

Question

Fine the open intervals on which the graph of f(x) = -x^5+20x^4-130x^3+280x^2-245x+724 is concave upward and those on which it is concave downward.
a. Concave upward (1,4) and (7, ∞); concave downward (-∞, 1) and (4,7)
b. Concave upward (-∞, 0) and (3,6); concave downward (0,3) and (6, ∞)
c. Concave upward (-∞, 1) and (4, 7); concave downward (1,4) and (7, ∞)
d. None of These

anonymous · Answer

The first derivative that I got is: -5x^4+80x^3-390x^2+560x+724 and the second is: -20[x^2(x-12)+1(39x-28)
The boxes are infinity signs, and I'm confused, please help.

anonymous · Answer

$$
 f' (x) = -5 x^4 + 80 x^3 - 390 x^2 + 560 x - 245 \
     f'' (x) = -20 x^3 + 240 x^2 - 780 x + 
     560 = -20 (x - 7) (x - 4) (x - 1)
      
      $$

anonymous · Answer

can you finish it now?

anonymous · Answer

Oh, Thanks! I see where I went wrong. I was so confused, thank you! I can do the rest I think. :)

anonymous · Answer

Excellent