Calculus

Limits & Continuity Solutions

f(x) = 4x / (x² - 49).
(A) List all critical numbers of f. If there are no critical numbers, enter 'NONE'.
Critical numbers =
(B) Use interval notation to indicate where f(x) is decreasing.
Note: Use 'INF' for ∞, '-INF' for -∞, and use 'U' for the union symbol.
Decreasing:
(C)List the x-values of all local maxima of f. If there are no local maxima, enter 'NONE'.
values of local maxima =
(D) List the x-values of all local minima of f. If there are no local minima, enter 'NONE'.
x values of local minima =
(E) List the x values of all inflection points of f. If there are no inflection points, enter 'NONE'.
Inflection points =
(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 all horizontal asymptotes of f. If there are no horizontal asymptotes, enter 'NONE'.
Horizontal asymptotes y =
(I) List all vertical asymptotes of f.
If there are no vertical asymptotes, enter 'NONE'.
vertical asymptotes x =
(J) 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: