- #1

- 120

- 0

## Homework Statement

On what intervals is the function f(x) = x^4 − 4x^3 both decreasing and concave up?

x < 0, 2 < x < 3

x < 3

x < 0, x > 2

x > 0, x < -3

2 < x < 3

## Homework Equations

## The Attempt at a Solution

I tried to get the derivative of f(x) to make it greater than 0

f'(x)=4x^3 -12x^2

0<4x^3-12x^2

0<3x^2(x-3)

o then take 3x^2 to the other side and end up with

0<x-3

3<x

I tried to get the concavity by taking the double derivative of f(x)

f''(x)=12x^2-24x

0<12x^2-24x

0<12x(x-2)

0<x-2

2<x

so the answer is 2<x<3?