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February 18th, 2019, 12:53 PM  #1 
Newbie Joined: Feb 2019 From: N/A Posts: 18 Thanks: 0 Math Focus: Calculus  "Finding Inflection Points" Math Problems Help 3
Ok this other inflection problem: Let h(x)=x^5+5x^4. For what values of x does the graph of h have a point of inflection? I am stuck on what to do after the second derivative which I found was: 6x^1+60x^2. I tried to factor it which gave me: 6(10x^2+x), but then I don't now how else to factor it until it becomes separated by two parentheses like my other previous problems. Could you help me out with the next steps? 
February 18th, 2019, 03:44 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,973 Thanks: 2224 
The first derivative of h is 5x^4 + 20x^3, so the second derivative is 20x³ + 60x², which is 20x²(x + 3). There is a point of inflection at x = 3 (the first derivative has a turning point there), but not at x = 0 (the first derivative doesn't have a turning point there). 

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