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February 18th, 2019, 12:53 PM   #1
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Exclamation "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?
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February 18th, 2019, 03:44 PM   #2
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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).
Thanks from topsquark and MikeAndIke
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