### Home > CALC > Chapter 9 > Lesson 9.2.1 > Problem 9-53

9-53.

*f* is concave up when *f* ″ is positive. Where is the given graph positive?

This is asking for the slope of the given graph at *x* = 5.

This is where *f* ″ changes sign. Where does the given graph change from negative to positive and vice versa?

*f* ′ has a minimum where its slope changes from negative to positive.

The slope of *f* ′ is *f* ″. So where does *f* ″ change from negative to positive?