1 answer

For what values of x is #f(x)=-x^2+xe^x# concave or convex?

Question:

For what values of x is #f(x)=-x^2+xe^x# concave or convex?

Answers

The function is concave up or convex for #x>0# and concave for #x<0#

Explanation:

#f(x)=-x^2+xe^x#
#f'(x)=-2x+e^x+xe^x#
#f''(x)=-2+2e^x+xe^x#
#f''(x)=0#
#0=-2+e^x(2+x)|+2#
#2=e^x(2+x)#
if #x=0#
#e^0=1#
#(2+0)=2#
#2*1=2#
#2=e^0(2+0)#
#f''(1)=2*e-2+e>0#
The function is concave up or convex for #x>0# and concave for #x<0#

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