It is very straightforward to obtain the equation of the tangent to a curve with equation provided you can differentiate .
Follow this worked example which shows you how to find the equation of the tangent to the curve with equation at the point where .
First, you have to find the -coordinate of the point where
(knowing to differentiate could be worth a mark)
The gradient at is the value of when ; in other words,
Now you need to find the equation of the line through with gradient .
To do this, you use the formula from the straight line section, often also written as
Find the equation of the tangent to the curve with equation at the point where .
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