Consider the differential equation dy/dx=x^2+4y-1. If y=f(x) is the solution to the differential equation, at what point does f have a relative maximum?

Question

Possible answers include:

 

A. (3, -2)

B. (0, 1/4)

C. (-2, -1)

D. (-5,-6)

Answer 1

y'=x²+4y-1   so   y''=2x+4y'

(3,-2)   --> y'=9-8-1=0        --> y''=6>0   min

(0,1/4) --> y'=4(1/4)-1=0    --> y''=0       test fails

(-2,-1)  --> y'=4-4-1=-1       --> (x=-2 is not a critical value)

(-5,-6)  --> y'=25-24-1=0    --> y''=-10<0 max