Minima maxima: a²y = x⁴

How to solve a²y = x⁴

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a2y=x4
 

Differentiate
a2y=4x3
 

Equate y' = 0 to determine the critical points (maxima or minima)
a2(0)=4x3

x=0
 

For x = 0
a2y=04

y=0
 

Hence,
critical point = (0, 0)
 

Check the neighboring points to determine whether (0, 0) is minimum or maximum. Set x = ±1:
a2y=(±1)4

y=+1a2   ←   above (0, 0)
 

Hence, the point (0, 0) is minimum.