College Algebra, Chapter 4, 4.2, Section 4.2, Problem 78

a.) Graph the function $P(x) = (x -1 )( x- 3)( x- 4)$ and find all the local extrema.
b.) Graph the function $Q(x) = (x - 1)( x - 3) (x - 4) + 5$ and use your answers to part (a) to find all local extrema

a.)


Based from the graph, the function has a local maximum at approximately $(1.75, 2.10)$ and local minimum at $(3.50, -0.60)$
b.)


Since the function in part(b) is the function in part(a) that is shifted 5 units upward, then only the $y$ coordinates of the local extrema will be added by 5. Thus, the function has a local maximum at $(1.75, 7.10)$ and local minimum at $(3.50, 4.40)$