Dalia S.

asked • 05/18/14

Find the slope of the secant line

The point P(9,7) 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 places after the decimal point)
if x=9.1, the slope of PQ is:
if x=9.01, the slope of PQ is:
if x=8.9, the slope of PQ is:
if x=8.99, the slope of PQ is:
 
B) Based on the above results, estimate the slope of the tangent line to the curve at P(9,7)
 

1 Expert Answer

By:

Leeland C. answered • 05/18/14

Mathematics and English expert through High School level classes

Dalia S.

for x=9.1 i got 0.166206 for the slope
x=9.01= 0.16662
x=8.9 = 0.1671323
x=8.99=0.166713 
 
all the above slopes are right however, im not getting part B of the question which asks to estimate the slope of the tangent line, how do you do it? 
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05/18/14

Dalia S.

i found all the slopes, however how do you go about doing part B of the question, which asks to estimate the slope of the tangent line? I would appreciate some help 
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05/18/14

Leeland C.

Like I said above, the slope of the tangent will be a number between the 8.99 slope and 9.01 slope. The slopes should all be EXTREMELY close together.
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05/18/14

Dalia S.

i understand but how do you know that?
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05/18/14

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