## anonymous 4 years ago 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: ??

1. Mertsj

|dw:1328845163296:dw|

2. anonymous

The 2nd one...:)

3. anonymous

And then (x, \sqrt{ x }+ 5 ) is |dw:1328845351408:dw|

4. Mertsj

slope at x= 16.9= .1248053 slope at x= 16.01=.1249805 slope at x = 15.9 = .12519593 slope at x = 15.99 = .1250195

5. anonymous

Thanks Mertsj!

6. anonymous

How do you find b?

7. Mertsj

Well based on looking at those slopes I would expect it to be between .1249 and .1251 so I guess my estimate would be .1250 What would yours be?

8. anonymous

yeah, not quite mine is .1255, but i believe yours is right!