1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Find interval where function is decreasing and concave up

  1. Sep 25, 2012 #1
    1. The problem statement, all variables and given/known data
    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

    2. Relevant equations


    3. 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?
     
  2. jcsd
  3. Sep 25, 2012 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Why greater than zero. Would that mean the function has positive slope or would it have negative slope? Would this mean that it is increasing or that it is decreasing?
     
    Last edited: Sep 25, 2012
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook