Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an answer does not exist, enter DNE.) f(x) = x² + 5x – 2

relative maximum
(x, y) = DNE

relativo minimum
(x, y) =

Relative minimum: , Relative maximum:

Step-by-step explanation:

First, we obtain the First and Second Derivatives of the polynomic function:

First Derivative

(1)

Second Derivative

(2)

Now, we proceed with the First Derivative Test on (1):

The critical point is .

As the second derivative is a constant function, we know that critical point leads to a minimum by Second Derivative Test, since .

Lastly, we find the remaining component associated with the critical point by direct evaluation of the function:

There are relative maxima.