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Interpretations of derivatives.
Example: Find out the equation of the tangent line to
x2 + y 2 =9
at the point (2, √5 ) .
Solution
We have to be given both the x & the y values of the point. Notice that this point does lie on the graph of the circle (you can verify by plugging the points into the equation) and thus it's okay to talk regarding the tangent line at this point.
Recall that to write the tangent line we required is the slope of the tangent line and it is nothing more than the derivative evaluated at the specified point.
Then the tangent line is.
y = √5 - 2/ √5 ( x - 2)
Now, let's work on some more examples.
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1+1
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