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

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!
RELATED QUESTIONS
find the point of inflection f(x)=... (answered by texttutoring)
f(x)=x^4-18x^2+4 Find all the points of inflection. Please help! (answered by Scriptor)
Find the critical points of function f(x) = ln(x)/x and describe the point of inflection... (answered by ikleyn)
find the largest open interval at which function is concave up or concave down and find... (answered by stanbon)
Find the equations of the tangent lines at all inflection points on the graph of:... (answered by Alan3354)
find the point of inflection f(x)= 1/4x^4 - x^3 +... (answered by jsmallt9)
Find point of inflection (x,y) if... (answered by ewatrrr)
Please Please Help! Find all the points of inflection (concavity) f(x)=... (answered by funmath)
consider the following function f(x)=4x^3+x^2-0.06x+7 find the two points on the graph... (answered by solver91311)