SOLUTION: Find all the points of inflection of the function f(x)=8x^2-2x^4 find point with smaller x-value find point with larger x value can someone help please

Click here to see ALL problems on Exponential-and-logarithmic-functions

Question 200749: Find all the points of inflection of the function
f(x)=8x^2-2x^4
find point with smaller x-value
find point with larger x value
can someone help please

Found 2 solutions by Alan3354, Earlsdon:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
Find all the points of inflection of the function
f(x)=8x^2-2x^4
find point with smaller x-value
find point with larger x value
----------------------
f(x)=8x^2-2x^4
The points of inflection are where the 2nd derivative = 0
f'(x) = 16x - 8x^3
f''(x) = 16 - 24x^2 = 0
x^2 = 2/3
Points of inflection at
x = � sqrt(6)/3
--> (sqrt(6)/3,40/9) (larger x)
and (-sqrt(6)/3,40/9) (smaller x)
------------
email via the thank you note with any questions.
--------------
PS The other tutor, Earlsdon, solved for the zeroes, not the points of inflection. His graph was great, tho.

Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
The graph of this function will give you the answers:

But you can also get the answers algebraically:
Substitute
The roots (zeros) occur at y = 0, so substitute this...
Solve for the x's, there should be four roots for this 4th degree polynomial. Factor out
Apply the zero product rule so that...
or
For , There are two roots at x = 0.
For , then and
So the four roots (zeros) are:

Compare these with the graph!
The inflection points (where the curve changes sign) are:

My appologies for the first answer about the points of inflection!