Find the critical points, domain endpoints, and local extreme values for the function
y=x^2/5(x+3)

a. What is/are the critical point(s) and domain endpoint(s) where f' is undefined?
b. What is/are the critical point(s) and domain endpoint(s) where f' is 0?
c. From the critical point(s) and domain endpoint(s), what is/are the points corresponding to local maxima?
d. From the critical point(s) and domain endpoint(s), what is/are the points corresponding to local minima?

a) , b) , , c) , d)

Step-by-step explanation:

a) Let derive the function:

is undefined when denominator equates to zero. The critical point is:

b) when numerator equates to zero. That is:

This equation shows two critical points:

,

c) The critical points found in point b) and the existence of a discontinuity in point a) lead to the conclusion of the existence local minima and maxima. By plotting the function, it is evident that corresponds to a local maximum. (See Attachment)

d) By plotting the function, it is evident that corresponds to a local minimum. (See Attachment)