Determine the total number of critical points of the function f(x)=(x+e^x)^k, where k>0 is an integer

Haley Madden 2022-07-23 Answered
Determine the total number of critical points of the function f ( x ) = ( x + e x ) k , where k > 0 is an integer
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Answers (2)

Tolamaes04
Answered 2022-07-24 Author has 12 answers
f ( x ) = k ( x + e x ) k 1 × ( 1 + e x ) = 0
has only one solution which is where x + e x = 0 and that is the point that you want to approximate.
The answer should be negative so x = 0.567 is problematic.
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Zoagliaj
Answered 2022-07-25 Author has 2 answers
At critical points f ( x ) = 0 so
0 = k ( x + e x ) k 1 × ( 1 + e x )
k and ( 1 + e x ) are positive so 0 = x + e x
x n = e x n + 1 so x 0.56714329
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