Question

Use the first derivative to find all critical points and use the second derivative to find all inflection points. Use a graph to identify each critical point as a local maximum, a local minimum, or neither. F(X)=x^5-5x^4+20

Answer 1

dy/dx = 5x^4-20x^3 = 0 so x^3(5x-20)=0 so x=0 or x=4 at inflection points.
d2y/dx2= 20x^3-60x^2 put in x=0 and it's = 0 therefore point of inflection and neither a maximum or a minimum, put in x=4 and it's positive so x=4 is a minimum