How would you find the minimum turning point of the function y = x^3 + 2x^2 - 4x + 10

The first step in solving the equation is to find the stationary points of the function, these are the points where the gradient is equal to zero. In order to find these points, first differentiate using the rule multiply by the power, take one off the power to get:dy/dx= 3x^2 + 4x - 4In order to find where this gradient is zero, make this equal to zero and then factorise to get:(3x-2)(x+2)=0In order for this to be true x must be either 2/3 or -2. These are the stationary points so one will be the maximum and one will be the minimum point that x cubed graphs have two turning points.To discover which is the minimum, we must differentiate the equation a second time:d2y/dx2= 6x+4If this is positive, then the gradient is increasing and thus this must be the minimum point on the graph. This is positive when x= 2/3 so this is the minimum, and y is equal to 230/27. The minimum turning point (2/3, 230/27)