1. ## Inflection Point

How would you find the inflection point for the following problem:

NOTE: I worked out most of this problem, it gives you the initial function and then asks you to do the following things:
(a)Find the intervals of increase and decrease.
(b)Find local maximum and minimum values.
(c)Find the interval of concavity and the inflection points.
(d)Use the information from (a)-(c) to sketch the graph.
-I did everything except find the inflection points and sketch the graph.-

h(x)=x^5-2x^3+x
h'(x)=5x^4-6x^2+1
h''(x)=20x^2-12x

H is increasing on: [-(infinity), 1/5] and [1,(infinity)]
H is decreasing on: [1/5, 1]

Local max at:
-1: h'(-1)=0
-1/5: h'(-1/5)=-.18432....
1/5: h'(1/5)=.18432

Local min at:
1: h'(1) = 0

h is concave up on intervals [-.77,0], [.77, (infinity)]
h is concave down on intervals [-(infinity), -.77], [0,.77]

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Let me know if you need any more information or if I made a mistake somewhere along the way.

2. For getting inflection points solve f''(x)=0

20x^3-12x=0
x(20x^2-12)=0
x=0,sqrt(3/5),-sqrt(3/5)