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The point P(8, −2) lies on the curve y = 2 7−x. (a) If Q is the point (x, 2 7−x), find the slope of the secant line PQ (correct to six decimal places) for the following values of x. (i) 7.9 mPQ = (ii) 7.99 mPQ = (iii) 7.999 mPQ = (iv) 7.9999 mPQ = (v) 8.1 mPQ = (vi) 8.01 mPQ = (vii) 8.001 mPQ = (viii) 8.0001 mPQ = (b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(8, −2). m = (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(8, −2).

The point P(8, −2) lies on the curve y = 2 7−x. (a) If Q is the point (x, 2 7−x), find the slope of the secant line PQ (correct to six decimal places) for the following values of x. (i) 7.9 mPQ = (ii) 7.99 mPQ = (iii) 7.999 mPQ = (iv) 7.9999 mPQ = (v) 8.1 mPQ = (vi) 8.01 mPQ = (vii) 8.001 mPQ = (viii) 8.0001 mPQ = (b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(8, −2). m = (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(8, −2).

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The point P ( 8 , − 2 ) lies on the curve y = 2 7 − x . (a) If Q is the point ( x , 2 7 − x ) , find the slope of the secant line P Q (correct to six decimal places) for the following values of x . (i) 7.9
m P Q =
(ii) 7.99
m P Q =
(iii) 7.999
m P Q =
(iv) 7.9999
m P Q =
(v) 8.1
m P Q =
(vi) 8.01
m P Q = ◻ − ⋯
(vii) 8.001
m P Q =
(viii) 8.0001
m P Q =
.. - (b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P ( 8 , − 2 ) .
m = −
◻ (c) Using the slope from part (b), find an equation of the tangent line to the curve at P ( 8 , − 2 ) . ◻

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