Suppose that
f(x) = 5 x^6 - 3 x^5.
(A) Find 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 increasing.
Note: Use 'INF' for \infty, '-INF' for -\infty, and use 'U' for the union symbol.
Increasing:
(C) Use interval notation to indicate where f(x) is decreasing.
Decreasing:
(D) Find the x-coordinates of all local maxima of f. If there are no local maxima, enter 'NONE'.
x values of local maxima =
(E) Find the x-coordinates of all local minima of f. Note: If there are no local minima, enter 'NONE'.
x values of local minima =
(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 inflection points of f. If there are no inflection points, enter 'NONE'.
x values of inflection points =
(I) Find all horizontal asymptotes of f. If there are no horizontal asymptotes, enter 'NONE'.
Horizontal asymptotes y =
(J) Find all vertical asymptotes of f. If there are no vertical asymptotes, enter 'NONE'.
Vertical asymptotes x =
