Find the absolute maximum value of the function f(x)=9(x-e^{x}).

tapetivk

tapetivk

Answered question

2021-12-03

Find the absolute maximum value of the function f(x)=9(xex).

Answer & Explanation

Mespirst

Mespirst

Beginner2021-12-04Added 17 answers

Step 1
We have f(x)=9(xex)
Then f(x)=9(1ex)
Now for the maximum value f'(x)=0
For
f'(x)=0
that is 9(1ex)=0
that is ex=1
This implies that x=0
Step 2
Now fx)=9ex
So f"(0)=-9(<0)
So at x=0 the function f has maximum
Now f(0)=9(0e0)=9
So the absolute maximum value of the function f is |f(0)|=|-9|=9

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