To find the local extrema of a polynomial function f(x) = anxn + an-1xn-1 + … + a2x2 + a1x + a0 (or any other function), you would apply the equation f ’(x) = 0. Consider the basic form of a quadratic equation: f(x) = ax2 + bx + c. Apply the equation above to this quadratic function and solve for x. The resulting equation should be familiar from algebra/pre-calculus. What did you call this equation and how is it related to the location of a local extrema on a quadratic function?
