Question

The position (in meters) of a particle is modeled by y=x^3-12.5x^2+51x-67.5, where xis in seconds. Find the max, min and point(s) of inflection.

Answer 1

for max/min, take first derivative, set equal to zero and solve for x , (2 answers)
put that x back into original equation

for pts of inflection, take second derivative, set equal to zero and solve for x (one solution for a cubic)
put that x value back into original to get that point of inflection