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[answered] 1) Suppose that: f(x)=ln(3+x^2) (A) Use interval notation t


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? =


 


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