Find the intervals of increase and decrease for the following function

Question

h(x)=(x^3)(x-1)^4
h'(x)=[(3x^2)(x-1)^4]+(4x^3)(x-1)^3

How do I find the zeros?

Thanks.

Answer 1

The zeros of the derivative or the zeros of the function ?
I will assume you want the zeros of the derivative.

factor it first
= x^2(x-1)^3[4x + 3(x-1)]
= x^2(x-1)^3(7x-3)
we set this equal to zero to get
x = 0, x = 1 and x = 3/7

remember that the function increases when the first derivative is positive, and decreases when that derivative is negative.
Can you take it from here ?

Answer 2

Do you factor it by taking the lowest ^ ? I can continue from there, thanks! :)

Answer 3

The answer key indicated that 0 is not a zero.

Answer 4

Your question was,
"how do I find the zeros"

x = 0 is a solution to h(x) = 0 and h'(x) = 0

Answer 5

If x=0, shouldn't it be used to determine the increase and decrease?