How do I find the equation of the tangent of a curve at a specific point.

The gradient is the rate of change at a specific point on the curve. Since the tangent is a straight line that touches the curve only once at a specific point, the gradient of the curve and the tangent will be the same at that point. We can find the equation of the tangent at any point on a curve by following the steps below: 1: Differentiating the equation of the curve i.e. finding d(f(x))/dx. 2: Substituting the x value of the point in the differentiated equation; we will get the gradient (m) of the curve at that point. 3: We then use the equation of a straight line: y-y1=m(x-x1) where y1 and x1 are the coordinates of the point and m is the gradient found in step 2.