Suppose that f(x) = ln(8x^2 + 5).
(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. If there are none, type "none". Critical value(s) =
(B) Find the x-coordinates of all local maxima of f. If there are no local maxima, enter none. If there are more than one, enter them separated by commas. If there are none, type "none". Local maxima at x =
(C) Find the x-coordinates of all local minima of f. If there are no local minima, enter none. If there are more than one, enter them separated by commas. If there are none, type "none". Local minima at x =
(D) Use interval notation to indicate where f(x) is increasing. If there is no such interval, enter none. Note: When using interval notation in WeBWorK, you use I for ∞, -I for -∞, and U for the union symbol. If there are no values that satisfy the required condition, then enter "{}" without the quotation marks. Increasing:
(E) Use interval notation to indicate where f(x) is decreasing. If there is no such interval, enter none. Decreasing:
(F) Use interval notation to indicate where f(x) is concave up. If there is no such interval, enter none. Concave up:
(G) Use interval notation to indicate where f(x) is concave down. If there is no such interval, enter none. Concave down:
(H) 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 =
(I) Find all horizontal asymptotes of f. If there are no horizontal asymptotes, enter none. If there are more than one, enter them separated by commas. Horizontal asymptote(s): y =
(J) Find all vertical asymptotes of f. If there are no vertical asymptotes, enter none. If there are more than one, enter them separated by commas. Vertical asymptote(s): x =
(K) Use all of the preceding information to sketch a graph of f. When you're finished, enter a "1" in the box below. Graph Complete: