Simple differentiation problem

[hancmarginis]

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[Ray Vickson]

Find a and b such that the function e^x*(ax+b) shares a point of extremum with the function x^2*e^x .

So differentiating the latter and finding its p.o.e's gives x= -2 or x=0.

Differentiating the former and plugging x= -2 in, gives:
f'(x) = e^x*(a+ax+b) = 0 for p.o.e
f'(-2)= a-2a+b=0
so a=b.
Now what?

I know this question is insultingly easy, but I cannot see where I've gone wrong. It's disgusting.

You have equated the x-values, but not the y-values; sharing a point means having the same x and y both.