Find the stationary points on y = x^3 + 3x^2 + 4 and identify whether these are maximum or minimum points.

First, you will need to differentiate the function with respect to x. Finding dy/dx.For polynomials, this is done by taking one away from the old power and multiplying the coefficient by the old power and removing any constant terms. This gives: dy/dx = 3x^2 + 6x this equation describes the rate of change of y with respect to x. In other words the gradient of the graph. This can be used to find the stationary points where the gradient is equal to zero. By setting dy/dx = 0 these points can be identified.3x^2 + 6x = 0.By solving this as quadratic equation, the following x values were calculated: x = 0, -2.By plugging these x values back into the original function, the corresponding y variables can be calculated. Giving coordinates (0, 4) and (-2,8).In order to identify whether these stationary points correspond to local maxima or minima, one must calculate d^2y/dx^2 by differentiating again to produced^2 y/ dx^2 = 6x + 6By calculating this for each x value, the result will tell you whether the point is a maxima (d^2y/dx^2 < 0) or a minima (d^2y/dx^2 > 0) as it represents the rate of change of the rate of change. For a maxima, the rate of change will be negative as the function immediately after the point will be decreasing, and for a minima it will be positive since the function will increase immediately after the point. If d^2y/dx^2 = 0 then it is undetermined.