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Social ScienceLet g(x) =x/x^2+75 ..g'(x) = Ax2 + B(x2 + 75)C, where A = B = C = g''(x) = Dx(x2 + E)(x2 + F)G, whereD = E = F = G =Find the interval(s) on which the graph of the function is concave upward and those on which it is concave downward. Enter the values for the endpoint(s) in the appropriate blanks and DNE in any empty blanks.The graph of the function is concave upward on the interval(s): (−∞, ∞)(−∞, a) (−∞, a](a, ∞)[a, ∞)(−∞, a) ∪ (b, ∞)(−∞, a] ∪ [b, ∞)(−∞, a) ∪ (b, c)(a, b) ∪ (c, ∞)(a, b)[a, b]None of the above.a = b = c = The graph of the function is concave downward on the interval(s):(−∞, ∞)(−∞, d) (−∞, d](d, ∞)[d, ∞)(−∞, d) ∪ (f, ∞)(−∞, d] ∪ [f, ∞)(−∞, d) ∪ (f, h)(d, f) ∪ (h, ∞)(d, f)[d, f]None of the above.d = f = h =
| x/x^2+75 |
g'(x) =
| Ax2 + B |
| (x2 + 75)C |
A =
B =
C =
g''(x) =
| Dx(x2 + E) |
| (x2 + F)G |
D =
E =
F =
G =
Find the interval(s) on which the graph of the function is concave upward and those on which it is concave downward. Enter the values for the endpoint(s) in the appropriate blanks and DNE in any empty blanks.
The graph of the function is concave upward on the interval(s):
a =
b =
c =
The graph of the function is concave downward on the interval(s):
d =
f =
h =
Expert Answer
The given function is
Image Transcriptionclose
g(x) x75
Obtain the first derivative as follows:
Image Transcriptionclose
d g'(x) dx275 d (x2+75)(x)(x2 +75) (x2+75) (x2 +75)(1)-x(2x) dx (x+75) -x275 where A 1,B= 75,C 2 (x+75)
Obtain the second deriva...
Image Transcriptionclose
-x275 g'(x) d 2 d (x2 + 75) 75)-(-~2 +75)4( (x2 +75) (62-75) (-2x) (x+75)-4x (2 +75)(-x? +75) - 75)- 4x(x2 +75)(-x? +75) +75 2х (-х* + 225 +75
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