Question

f(x) = 3x^3 - 9x + 5

find the:
1) zeroes or undefined values

2) intervals where the function is greater than zero

3) intervals where the function is less than zero

4) coordinates of all maxima and minima

5) intervals where the function is increasing

6) intervals where the function is decreasing

i'm not sure how to find this information using the equation. can someone help and explain? i'm allowed to use a graphic calculator.

Answer 1

graph it, and the graph will answer all those questions.

I am not certain how far you are in calculus. You can get them all analytically, also. Try your calculator first.

Answer 2

1) 1.3170051, 0.64500159, -1.962007
2) when x>1 and x= 0,-1
3) when x<-1 and x=-1
4) ???
5) x<1 x>1
6) x<1

is this correct? and i'm not sure how to find the maxima and minima

Answer 3

maxima and minima are where f' = 0

f = 3x^3 - 9x + 5
f' = 27x^2-9 = 9(3x^2-1)
so, when 3x^2-1 = 0, f has a max or a min.