Answer:
The derivative (or gradient function) describes the gradient of a curve at any point on the curve. Similarly, it also describes the gradient of a tangent to a curve at any point on the curve.
To determine the equation of a tangent to a curve:
Find the derivative using the rules of differentiation.
Substitute the \(x\)-coordinate of the given point into the derivative to calculate the gradient of the tangent.
Substitute the gradient of the tangent and the coordinates of the given point into an appropriate form of the straight line equation.
Make \(y\) the subject of the formula.
The normal to a curve is the line perpendicular to the tangent to the curve at a given point
Explanation: