Home > CALC > Chapter 9 > Lesson 9.2.1 > Problem 9-53
9-53.
The graph below shows f". Use it to answer the following questions. Homework Help ✎
Over what interval(s) is f concave up?
Estimate f '''(5).
At what x-value(s) does f have a point of inflection?
At what x-value(s) does f ' have a minimum value?
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?