February 18th, 2019, 04:46 PM  #1 
Newbie Joined: Feb 2019 From: N/A Posts: 18 Thanks: 0 Math Focus: Calculus  Second Derivative Test Problem
Let h be a twice differentiable function, and let h(4)=3, h'(−4)=0, and h''(4)=0. What occurs in the graph of h at the point (4,3)? So, what should I start doing first? 
February 18th, 2019, 04:55 PM  #2  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,271 Thanks: 934 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
The second derivative is 0 when the first derivative is 0. What does that mean? Dan  
February 18th, 2019, 05:15 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,969 Thanks: 2219 
As the first derivative at (4, 3) is zero, the function has a horizontal tangent there. Further information would be needed to determine whether (4, 3) is a turning point or a point of inflection. 
February 18th, 2019, 05:52 PM  #4 
Newbie Joined: Feb 2019 From: N/A Posts: 18 Thanks: 0 Math Focus: Calculus  So is (4,3) a maximum or minimum point? Or is there not enough information to determine it?
Last edited by skipjack; February 18th, 2019 at 06:09 PM. 
February 18th, 2019, 06:11 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,969 Thanks: 2219 
It could be a maximum point, minimum point or point of inflection. Further information would be needed to determine which applies.


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