The point P(16,8) lies on the curve y=√(x)+4Let Q be the point (x,√x+4).A.) Find the slope of the secant line PQ for the following values of x. (Answers should be correct to at least 6 decimal places.)If x=16.1, the slope of PQ is: and if x=16.01, the slope of PQ is: and if x=15.9, the slope of PQ is: and if x=15.99, the slope of PQ is: B.) Based on the above results, guess the slope of the tangent line to the curve at P(16,8).

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Asked Sep 9, 2019
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The point P(16,8) lies on the curve y=√(x)+4

Let Q be the point (x,√x+4).

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

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

B.) Based on the above results, guess the slope of the tangent line to the curve at P(16,8).

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Expert Answer

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Step 1

The points P= (16,8) and Q= (x, x^1/2+4) lies on the curve which is given by:

+4
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+4

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Step 2

If the secant line is passing through the points P = (x1, y1) and Q = (x2, y2) then the slope of the secant PQ is given by:

y2-
m =-
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y2- m =-

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Step 3

Now, at x=16.1 the point Q is (16.1,8.01). then the slope of secant l...

8.01-8
16.1-16
0.01
0.1
0.1
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8.01-8 16.1-16 0.01 0.1 0.1

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