How do I find dy/dx for a given equation, once this is found how do I find the value of x such that dy/dx = 0.

From a given equation y = mx + c. Finding dy/dx allows us to see the gradient of the curve. In order to do this we can follow the formula:When y = xⁿ , dy/dx = nx^{n-1 .} Let us use this in a real scenario. Say we are given the equation y = 3x² - 6x + 4. We can break this down into stages. First let us differentiate the 3x². Here the n = 2. So we bring the 2 to the front and subtract 1 from the power: so differentiating 3x² we have 6x. Now we do the same for -6x. Here the n = 1 so we bring to the 1 to the front and subtract 1 from the power: so differentiating -6x we have -6 (-6x⁰ = -6). Differentiating a constant results to cancelling that constant so differentiating the 4 results in 0 (as the gradient of a constant function is always 0). Putting all this together we have dy/dx = 6x -6. Now to find the value of x such that dy/dx = 0. We have our dy/dx as shown. We then set dy/dx = 0 and solve the equation. We therefore have 6x - 6 = 0. This implies that 6x = 6. So therefore x =1.