The point P ( 16 , 7 ) lies on the curve y = √ x + 3 . If Q is the point ( x , √ x + 3 ) , find the slope of the secant line P Q for the following values of x . If x = 16.1 , the slope of P Q is: and if x = 16.01 , the slope of P Q is: and if x = 15.9 , the slope of P Q is: and if x = 15.99 , the slope of P Q is: Based on the above results, guess the slope of the tangent line to the curve at P ( 16 , 7 ) .