Find the absolute minimum value of the function f(x)=2e^{x^{2}-2x+1} on

David Lewis

David Lewis

Answered question

2021-12-09

Find the absolute minimum value of the function f(x)=2ex22x+1 on the domain [-1,2].

Answer & Explanation

zesponderyd

zesponderyd

Beginner2021-12-10Added 41 answers

Step 1
Given function is:
f(x)=2ex22x+1
To find the absolute minimum value of the function in the domain of [-1,2]
Step 2
Now calculate the minimum value,
f(x)=2ex22x+1
f(x)=2e(x1)2
The maximum value of (x1)2 is not defined but the minimum value of (x1)2 is 0 at x=1
Therefore, the minimum value of f(x)=2ex12 is also occurs at x=1
The corresponding minimum value of f(x) at x=1,
f(1)=2e(11)2
=2×1
=2
Thus, the absolute minimum value of the function is 2

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