Given the function f(x) = 2x³ + 3x² − 12x − 7, complete these steps:

a. Graph using [−10, 10]1 by [−10, 10]1 and [−10, 10]1 by [−20, 20]2.

b. Fill in this table:

c. Approximate the x intercepts and y intercept to two decimal places.

d. Find the relative maximum and relative minimum points.

e. Find the intervals over which f (x) is increasing.

f. Find the intervals over which f(x) is decreasing.

g. Find any inflection points.

h. Find the intervals over which the graph of f(x) is concave upward.i. Find the intervals over which the graph of f(x) is concave downward.

j. Show that the concavity changes from upward to downward, or vice versa, when x moves from a little less than the point of inflection to a little greater than the point of inflection.

k. Find the largest and smallest values for this function for −4 ≤ x ≤ 2.

Transcribed Image Text:

X f(x) f'(x) f"(x) -4 -2 -1 0 1 2