How do you find the points where the graph of the function #(x^(2))/(e^(x))# has horizontal tangents?

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Answer 1 · 2018-06-24T17:29:44

#x=0# or #x=2#

#f(x)=x^2/e^x#
by the Quotient rule wqe get

#f'(x)=(2xe^x-x^2e^x)/(e^x)^2#
writing this as

#f'(x)=(e^x(2x-x^2))/(e^x)^2#

#f'(x)=(2x-x^2)/e^x#
so #f'(x)=0# if

#2x-x^2=0#
or

#x(2-x)=0#
so we get

#x=0# or #x=2#