1) Suppose that: f(x)=ln(3+x^2)

(A) Use interval notation to indicate where f(x) is concave up.

Note: When using interval notation in WeBWorK, you use I for infinity, -I for negative infinity, and U for the union symbol. If there are no values that satisfy the required condition, then enter "{}" without the quotation marks. Concave up:

(B) Use interval notation to indicate where f(x) is concave down.

Concave down:

(C) Find all inflection points of f. If there are no inflection points, enter -1000. If there are more than one, enter them separated by commas. Inflection point(s) x at =

2)

Let f(x)=-x^4 - 6x^3 +5x - 4. Find the open intervals on which f is concave up (down). Then determine the x-coordinates of all inflection points of f.

1.	is concave up on the intervals
2.	is concave down on the intervals
3.	The inflection points occur at x =

Notes: In the first two, your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-inf, 2), (3,4), or the word "none".

In the last one, your answer should be a comma separated list of x values or the word "none".

3) Suppose that

f(x)= (5e^x)/(5e^x + 3)

(A) Find all critical values of f. If there are no critical values, enter None. If there are more than one, enter them separated by commas. Critical value(s) = (B) Use interval notation to indicate where f(x) is concave up. Concave up: (C) Use interval notation to indicate where f(x) is concave down. Concave down: (D) Find all inflection points of f. If there are no inflection points, enter None. If there are more than one, enter them separated by commas. Inflection point(s) at x =