The point P7 2 lies on the curve y 26 x a If Q is the point

The point P(7, 2) lies on the curve y = 2/(6 x). (a) If Q is the point (x, 2/(6 x)), use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x.

(i)    6.9

m_PQ = 1

(ii)    6.99

m_PQ = 2

(iii)    6.999

m_PQ = 3

(iv)    6.9999

m_PQ = 4

(v)    7.1

m_PQ = 5

(vi)    7.01

m_PQ = 6

(vii)    7.001

m_PQ = 7

(viii)    7.0001

m_PQ = 8

(b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at

P(7, 2).

m = 9

(c) Using the slope from part (b), find an equation of the tangent line to the curve at

P(7, 2).

Solution

the answers of (A)

i. 6.9 = 2.222222
ii 6.99 = 2.020202
iii. 6.999 =2.002002

iv.6.9= 2.000200

v.7.1= 1.818182

vi.7.01= 1.980198

vii.7.001= 1.998002

vii.7.0001= 1.999800

As u observe the answers what we got ,the values were closer to X=7.the slopes get closer to 2.0

Now that you know the slope is 2 and a point on the tangent like is (7,-2), you can find the slope of the line using your favorite point-slope technique.

I\'ll use m (x-x1) = y - y1

2 (x - 7) = y + 2
y = 2x -16