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 2239 views around the world You can reuse this answer Creative Commons License