I need help with this math question.
x^3-8x^2<0

9514 1404 393

  (-∞ < x < 0) ∪ (0 < x < 8)

Step-by-step explanation:

Factoring the inequality gives you ...

  x²(x -8) < 0

The x-intercepts of the curve described by the left-side expression are 0 and 8, values that make the factors zero. The intercept at x=0 has multiplicity 2, so the curve does not cross the x-axis there.

Since this is an odd-degree polynomial with a positive leading coefficient, its general shape is rising to the right. That means the left-side expression will be negative for x-values less than the first x-intercept, and for x-values between the x-intercepts.

The solution is ...

  (-∞ < x < 0) ∪ (0 < x < 8)

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)