SOLUTION: Hai sir, please help me on this problem "Determine all inflection points of function f defined by, f(x) = x4 + x3 + 2 a)(0,1) and (1/2, 15/31) b)(0,1) and (1/3, 12/32) c)

Algebra ->  Testmodule -> SOLUTION: Hai sir, please help me on this problem "Determine all inflection points of function f defined by, f(x) = x4 + x3 + 2 a)(0,1) and (1/2, 15/31) b)(0,1) and (1/3, 12/32) c)      Log On


   

Question 397766: Hai sir, please help me on this problem
"Determine all inflection points of function f defined by, f(x) = x4 + x3 + 2
a)(0,1) and (1/2, 15/31)
b)(0,1) and (1/3, 12/32)
c)(0, 2) and ( -1/2, 31/16)
d)None of these
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
df%2Fdx++=4x%5E3+%2B+3x%5E2 ==> d%5E2f%2Fdx%5E2+=+12x%5E2+%2B+6x+.
Set the 2nd derivative to 0:
d%5E2f%2Fdx%5E2+=+12x%5E2+%2B+6x++=+6x%282x+%2B+1%29+=+0 ==> x = 0, -1/2.
When x = -1, d%5E2f%2Fdx%5E2+%3E+0,
when x = -1/4, d%5E2f%2Fdx%5E2+%3C+0, and
when x = 1, d%5E2f%2Fdx%5E2+%3E+0.
Therefore there are changes of concavity in the intervals (-infinity, -1/2), (-1/2, 0), and (0, infinity). To find the y-coordinates, substitute x = 0 and x = -1/2 in to original function.
The answer is c.