What is the equation of the tangent line of #f(x)=sin x + sin^2 x# at #x=0#?
This problem can be tackled in 3 steps:
1. Figure out the gradient of the line using the derivative of the function and the given
2. Use the given
3. Put values into the standard equation of a straight line.
The equation of a line
1. We'll begin by working out
Where the chain rule has been used on the
Since we want to find the tangent at
Step 1 is complete.
2. We must now find
Thus we have our value for
3. We can now write:
Indeed we see that if we plot both on the same graph we get a line intersection at a tangent exactly where we would expect: