Question

Where do the relative minimum and the relative maximum occur for the unknown function y=f(x)? The only information we have about the function is: (1) The critical points are x=3 and x=-2, and (2) The second derivative is f''(x)=2x-1

Answer 1

$f''(3)=2\cdot3-1=6-1=5>0 \Rightarrow \text{minimum}\\ f''(-2)=2\cdot(-2)-1=-4-1=-5$