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 6506 views around the world You can reuse this answer Creative Commons License