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.

see below

step-by-step explanation:

x+2> 6

subtract 2 from each side

x+2-2 > 6-2

x > 4

there is an open circle at 4 since is it is greater than and the line goes to the right

d

step-by-step explanation: