Respuesta :
f'(x) = 2x = 0 , x = 0 - so there is a turning point at x = 0
f"(x) = 2
so there is a relative minimum at x = 0
f"(x) = 2
so there is a relative minimum at x = 0
The given function f has a relative minimum and this can be determined by differentiating the given function.
Given :
Function --- [tex]\rm f(x) = x^2+e^{-2}[/tex]
The following steps can be used in order to determine the correct statement about the given function:
Step 1 - Write the given function.
[tex]\rm f(x) = x^2+e^{-2}[/tex] --- (1)
Step 2 - Differentiate the above function with respect to 'x'.
f'(x) = 2x --- (2)
Step 3 - Now, equation the above differential function to zero.
2x = 0
x = 0
Step 4 - Now, differentiate the expression (2) with respect to 'x'.
f"(x) = 2 >0
Therefore, from the above steps, it can be concluded that f has a relative minimum. So, the correct option is d).
For more information, refer to the link given below:
https://brainly.com/question/5245372
