Question

Use the first derivative rule to find the values of x for which

f(x) = 1/3 x^3 + 3/2 x^2 - 18 x + 3

is increasing and decreasing.

Hint: Use what you know about the shape of cubic polynomial graphs from Algebra and Precalculus.

. The function f is increasing for the following values of x:

it should look something like a 14 years ago

Answer 1

here's another one lol

Answer 2

yea!
f(x) = 1/3 x^3 + 3/2 x^2 - 18 x + 3
f'(x) = x^2 + 3x - 18
when f is increasing
x^2 + 3x - 18 > 0
critical points
(x + 6)(x - 3) = 0
x = -6 and x = 3
f increasing when x < -6
when x is in between -6 and 3
x is decreasing
when x is > 3
its increasing
hmm - i'm getting a bit confused here - ill draw a rough graph