Find the turning point of y = x + 1 + 4/x2 and describe the nature of the turning point

To find the turning point of the equation, it should be recognised that we desire the point at which the gradient is 0. The gradient is given by dy/dx and hence we differentiate the equation with respect to x to yield the following:dy/ dx = 1 -8 x^(-3) Equating dy/ dx to 0 and solving for x, we get: x = 2 Substituting this into the original curve equation we can get y. The nature of the turning point can be determined by taking a second derivative i.e. find d^2y/ dx^2. The answer is found by substituting x = 2 into this expression, yielding d^2y/dx^2 > 0 and hence it is a minimum.