What is the relationship between the First and Second Derivatives of a Function? Calculus Graphing with the Second Derivative Relationship between First and Second Derivatives of a Function 1 Answer Wataru Aug 30, 2014 Since #f''# is the first derivative of #f'#, #f''# tells us about the increasing/decreasing behavior of #f'#. Answer link Related questions Question #64fc4 What are the first two derivatives of #y = 2sin(3x) - 5sin(6x)#? What is the second derivative of the function #f(x)=sec x#? If #f(x)=sec(x)#, how do I find #f''(π/4)#? What is the second derivative of #g(x) = sec(3x+1)#? How do you use the second derivative test to find the local maximum and minimum for... What is the first and second derivative of #1/(x^2-x+2)#? What is the second derivative of #x/(x-1)# and the first derivative of #2/x#? What does the 2nd Derivative Test tell you about the behavior of #f(x) = x^4(x-1)^3# at these... F(x)=(x^2-2x+4)/ (x-2), f' (x)=(x^2-4x)/(x-2)^2 , f'' (x)=8/(x-2)^3 How to find the domain of... See all questions in Relationship between First and Second Derivatives of a Function Impact of this question 5781 views around the world You can reuse this answer Creative Commons License