Question #282183
1.     Determine the critical points of each of 




1
Expert's answer
2021-12-23T16:04:10-0500

for example:

f(x)=x2exf(x) = x^2e^x


then:

f(x)=2xex+x2ex=x(2+x)ex=0f'(x) =2xe^x+ x^2e^x=x(2+x)e^x=0


at critical point x=0x=0 :

f'(x) changes its sign from "-" to "+", so this is local minimum


at critical point x=2x=-2 :

f'(x) changes its sign from "+" to "-", so this is local maximum


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