Slope of Tangent Line : It is the next major interpretation of the derivative. The slope of the tangent line to f ( x ) at x = a is f ′ ( a ) . Then the tangent line is given by,

                                           y = f ( a ) + f ′ ( a ) ( x - a )

Example :  Determine the tangent line to the given function at z = 3 .

Solution : The derivative is,

Now all that we require is the function value & derivative (for the slope) at z = 3 .

R (3) =√7                                                           m = R′ (3) =  5 /2√ 7

Then the tangent line is,

y = √7 +     5/2√7(z-3)