Let f(x) = -2x3 - 9x2 - 12x + 3. Find thefollowing:
a) The domain of f Answer can be an interval or inwords
b) The y-intercept Answer must be a point
c) f '(x)
d) The critical numbers, if any.
e) The open interval(s) where the function is increasing and theopen interval(s) where the function is decreasing. Theanswer to this question will be accepted in one of twoways:
1) Show the number line with the critical numbers alongwith the open intervals, the test values (don't need to showplugging test values into function), and state where the numberline is + or -.
2) Show the number line with the critical numbers alongwith the open intervals, evaluate at your test values and state theopen intervals where the function is increasing ordecreasing.
f) State the relative maximum/relative minimum point, if any.The answer must be an ordered pair. Hence,show the work on obtaining the y-value and state order pair(s) thatis are a relative minimum and a relative maximum. If there are norelative extreme points, then state “no relativeextreme”.
