How do you find the local maximum and minimum values of f ' (x) = (x^2 -9)? Calculus Graphing with the Second Derivative Relationship between First and Second Derivatives of a Function 1 Answer anantha n. · Monzur R. Feb 13, 2018 at local max or min f'(x) is zero. => x^2 -9 = 0 => x^2 = 9 => x = +-sqrt9 = +- 3 so at x =+- 3 , the function is either max or min (locally). Answer link Related questions What is the relationship between the First and Second Derivatives of a Function? 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... See all questions in Relationship between First and Second Derivatives of a Function Impact of this question 2436 views around the world You can reuse this answer Creative Commons License