Question

Consider the function f(x) = x^3 - 6x^2 + 9

(a) Find intercepts:

(b) Find the first derivative of f and identify the critical values.

(c) Construct a sign chart for the first derivative. Find the intervals where f(x) is increasing and the intervals where f(x) is decreasing, and express the answer using interval notation. Find all local extremum.

(d) Find the second derivative of f(x), and find all zeros of the second derivative.

(e) Construct a sign char for the second derivative, and find the intervals where f(x) is concave upward and the intervals where f(x) is concave downwa

Answer 1

A)TO FIND THE INTERCEPTS :
x intercepts (x,0), to get it ... =====>set (y)=0 and solve for x
y intercepts (0,y) ,to get it ... =====>set(x)=0 and solve for y

Answer 2

ok I have x=0, x=3 but I don't know how to find y

Answer 3

why ,Which part are you having troubles in ?

Answer 4

I plug in 0 for x and I only get 0. For example I type in 0^3-6(0)^2+9(0) = 0 is that how I get the y or do I have to do the derivative to get y?

Answer 5

Just need a refresher on this. I am totally spazzing out.

Answer 6

Why did you multiply the 9 by zero ?

Answer 7

oh forgot to type it in original equation. it's f(x)=x^3-6x^2+9x