Dr. Deontae Koelpin V
Jan 12, 2025
At x=0, which of the following is true of the function f defined by f(x)=x^2+e^-2x?
At ( x = 0 ), which of the following statements is true for the function ( f ) defined by ( f(x) = x^2 + e^{-2x} )?
a) ( f ) is increasing
b) ( f ) is decreasing
c) ( f ) is discontinuous
d) ( f ) has a relative minimum
e) ( f ) has a relative maximum
I would appreciate it if someone could show the work involved in determining the correct answer, as I would like to understand the reasoning behind it.
2 Answers
Feb 03, 2025
f(x)=x^2+e^-2x
f'(x)=2x+(e^(-2x))*-2
when x=0, f'(x)=-2.
B) f(x) is decreasing at x=0 because f'(x) is negative.
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