Consider the function y = 2x^3-3x^2+9x+5.

Question

1. Find where the function is increasing, where the function is decreasing, and calculate all relative extrema (local max and local min)
2. Find where the function is concave up, where the function is concave down, and find the inflection points.

Answer 1

y = 2x^3-3x^2+9x+5
y' = 6x^2-6x+9
y" = 12x-6

Now, just apply the basic rules
extrema at y'=0 and y"≠0
y increasing where y' > 0
y concave up where y" > 0
inflection points at y"=0

Note: There may not be any extrema, and so on. Sometimes the required conditions do not exist.