Step-by-step explanation:
R'(x) = 5x³ − 60x²
A) R"(x) = 15x² − 120x
0 = 15x² − 120x
0 = 15x (x − 8)
x = 0 or 8
B) R"(-1) = 135
R"(1) = -105
R"(x) changes signs around x = 0, so x = 0 is an inflection point.
R"(7) = -105
R"(9) = 135
R"(x) changes signs around x = 8, so x = 8 is an inflection point.
