Question 191203: I really need help on this problem so if you guys would be so kind to help!
Thanks
what is the x-coordinate of the point of inflections of the graph of y= (1/10)x^5 + (1/20)x^4 - (3/10)?
a) -4 b) -3 c) -1 d) -3/10 e) 0
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
 = \frac{1}{10} x^5 + \frac{1}{20}x^4 - \frac{3}{10})
This is a polynomial function, hence it is both continuous and contiuously differentiable over the entire domain which is the set of real numbers. Also it is (at least) twice differentiable. Hence, determining the point(s) of inflection is a job, not for Superman, but for the Second Derivitive Test.
Take the first derivitive:
 = \frac{1}{2} x^4 + \frac{1}{5}x^3 )
Now take the second derivitive:
 = 2x^3 + \frac{3}{5}x^2 )
A necessary condition for an inflection point is that  = 0) , so:
 = 0)
Hence, potential inflection points are at  and 
A sufficient condition for an inflection point is that ) and ) have opposite signs in the neighborhood of 
You should check this work, but I used Excel, put in the formula for ) and checked -.01 and .01, numbers in the neighborhood of 0 -- both positive, so 0 is not and inflection point. Checking -.31 and -.29 yielded a positive and a negative value, hence  is an inflection point.
John
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