Question

graph the function ( y = x^{2}-2x - 8 ) by identifying the domain and any symmetries, finding the derivatives ( y ) and ( y ), finding the critical points and identifying the functions behavior at each one, finding where the curve is increasing and where it is decreasing, finding the points of inflection, determining the concavity of the curve, identifying any asymptotes, and plotting any key points such as intercepts, critical points, and inflection points. then find coordinates of absolute extreme points, if any.

( y = 2x - 2 )

find the second derivative ( y ).

( y = 2 )

identify any critical points. select the correct choice below and, if necessary, fill in the answer box to complete your choice.

○ a. the critical point(s) occur(s) at ( x = )___

(use a comma to separate answers as needed.)

○ b. there are no critical points

Explanation:

Step1: Find critical points

Critical points occur where \(y' = 0\). Given \(y'=2x - 2\), set \(y'=0\):
\(2x-2 = 0\)
\(2x=2\)
\(x = 1\)

Answer:

A. The critical point(s) occur(s) at \(x = 1\)