Find the stationary points on the curve: y = x^3 + 3x^2 +2x+5
Firstly differentiate the function:f(x) = x3 + 3x2 + 2x + 5 (function)f'(x) = 3x2 + 6x + 2 (gradient function)
Stationary points are points where the graph has a gradient of zero
3x2 + 6x + 2 = 0
In order to find the x-values we need to solve the quadratic equation:a = 3, b = 6, c =2 ----> sub into the equation (will explain on whiteboard)Use quadratic equation to find x = -1 +/- root(3)/3
Finally sub in the x - values into the initial function to find the corresponding y values. Done!
NC
