Determine the nature of the stationary points for y = x4 − 8x3 − 3x2 + 36.

Here are the solutions for the given problems.

Problem (b): Determine the nature of the stationary points for $y = x^4 - 8x^3 - 3x^2 + 36$.

Step 1: Find the first derivative.

$$\frac{dy}{dx} = \frac{d}{dx}(x^4 - 8x^3 - 3x^2 + 36) = 4x^3 - 24x^2 - 6x$$

Step 2: Find the x-coordinates of the stationary points by setting the first derivative to zero.

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