Using the derivative to find the gradient of a curve

• To find the gradient of a curve?y=?f(x)?at any point on the curve, substitute the?x?coordinate?of the point into the derivative?f'(x)

Using the derivative to find a tangent

• At any point on a curve, the?tangent?is the line that goes through the point and has the same gradient as the curve at that point

• For the curve y = f(x), you can find the equation of the tangent at the point (a, f(a)) using

Using the derivative to find a normal

• At any point on a curve, the?normal?is the line that goes through the point and is?perpendicular?to the tangent at that point

• For the curve y = f(x), you can find the equation of the normal at the point (a, f(a)) using