Differentiation

Finding equations to normals - differentiation

1 -simplify and differentiate

2-find gradient to tangent but subbing x value in coordinates into the x

3-neg recip = gradient of normal

4- sub coordinates

Finding stationary points on a graph

To find stationary points, set the derivative equal to zero and solve for the x-values. Then find corresponding y-values by substituting the x-values back into the original function.

Finding minimum and maximum values on a graph

To find minimum and maximum values, analyze the derivative: locate stationary points by setting the derivative to zero, determine the second derivative to test concavity, and evaluate the function at these points.

How to find coordinates when dy/dx = 0

To find coordinates when dy/dx = 0, identify the x-values where the derivative is zero (stationary points). Then, substitute these x-values back into the original function to find the corresponding y-values.

Finding the equation of a tangent

By finding your gradient by subbing the x value and then y=mx+c