Question

What is the relative maximum value of the function f(x) = x^3 – 6x^2 + 9x – 12?
A. f(x) has a relative maximum value at x = 3, and its value is f(3) = -12.
B. f(x) has a relative maximum value at x = 3, and its value is f(3) = -8.
C. f(x) has a relative maximum value at x = 1, and its value is f(1) = -12.
D. f(x) has a relative maximum value at x = 1, and its value is f(1) = -8.

Answer 1

@UnkleRhaukus can u help?

Answer 2

can you factorise that?

Answer 3

no

Answer 4

can you find f(3) and f(1) ?

Answer 5

yes

Answer 6

for f(3) I got -12 and for f(1) I got -8

Answer 7

ok good, that rules out B. and C.

Answer 8

ok

Answer 9

now can you tell me if f(∞) approaches ∞ or -∞

Answer 10

positive infinity

Answer 11

right, and
does if f(-∞) approaches ∞ or -∞

Answer 12

negative infinity

Answer 13

okay

Answer 14

so its A right?

Answer 15

i cant remember the proper way to do this question , sorry

Answer 16

if we also look at f(0)

Answer 17

maybe its more like this