Question

The point P(16 , 9 ) lies on the curve y = \sqrt{ x } + 5. Let Q be the point (x, \sqrt{ x }+ 5 ).

a.) Find the slope of the secant line PQ for the following values of x. (Answers here should be correct to at least 6 places after the decimal point.)

If x= 16.1, the slope of PQ is: ?
If x= 16.01, the slope of PQ is:?
If x= 15.9, the slope of PQ is:?
If x= 15.99, the slope of PQ is:?

b.) Based on the above results, estimate the slope of the tangent line to the curve at P(16 , 9 ).

Answer: ??