# Let 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 =

Question
32 views
Let 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
, where
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)

(−∞, 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

check_circle

Step 1

The given function is

Step 2

Obtain the first derivative as follows:

Step 3

Obtain the second deriva...

### Want to see the full answer?

See Solution

#### Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in