local min, local max, inflection points, long and hard problem?

Question

Suppose that f(x) = 11 - 3 ln(x)

(A) List all the critical values of f(x).

(B) Use interval notation to indicate where f(x) is increasing.
Increasing:

(C) Use interval notation to indicate where f(x) is decreasing.
Decreasing:

(D) List the x values of all local maxima of f(x).
x values of local maximums =

(E) List the x values of all local minima of f(x).
x values of local minimums =

(F) Use interval notation to indicate where f(x) is concave up.
Concave up:

(G) Use interval notation to indicate where f(x) is concave down.
Concave down:

(H) List the x values of all the inflection points of f.
x values of inflection points =

Answer 1

f(x) = 11 - 3ln(x) for x > 0

f '(x) = - 3/x <0 for x > 0

f is a decreasing function, no max, no min

f ''(x) = 3/x² > 0

f is concave up , no inflection point