Applications in calculus
- $ m = f'(a) $
where m is the slope of the tangent line.
The full equation for the tangent line is:
- $ y = f'(a)(x-a) + f(a) $.
The tangent can alternatively be found (as long as the x-coordinate of the point A is given and the equation of the curve) by substituting x into the equation to find y. We can then differentiate the equation of the curve, substituting x in to find the gradient. We can then write the standard equation of a straight line using our existing known values as:
- $ y = m (x) + c $
We can then rearange to find c and find the equation of the tangent.