The point P(6,-3) lies on the curve y5-x e point (x₁ - x). find the slope of the secant line PQ (correct to six decimal places) for the following values of x. (1) 5.9 (a) If Q is the point (x.. (ii) 5.99 (iii) 5.999 (iv) 5.9999 MpQ (v) 6.1 MpQ (vi) 6.01 3.333333 (vii) 6.001 13.030303 = 2.99999 3.003003 = 2.727272 (viii) 6.0001 2970297 MpQ = 2.007003 12.00700 x X

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
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Please solve (iv), (v), and (viii)

The point P(6,-3) lies on the curve y =
(a) If Q is the point x,
(1) 5.9
PQ
e point (x₁53x). find the slope of the secant line PQ (correct to six decimal places) for the following values of x.
5-x,
(ii) 5.99
"PQ
(iii) 5.999
PQ
(v) 6.1
=3.030303
(iv) 5.9999
MpQ
(vi) 6.01
= 3.003003
MpQ
13.333333
(vii) 6.001
MpQ
= 2.727272
2.99999
(viii) 6.0001
2.970297
= 2.997003
1.99700
x
X
5-x
X
(b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(6, -3).
m=3
(c) Using the slope from part (b), find an equation of the tangent line to the curve at P(6, -3).
y = 3x - 21
Transcribed Image Text:The point P(6,-3) lies on the curve y = (a) If Q is the point x, (1) 5.9 PQ e point (x₁53x). find the slope of the secant line PQ (correct to six decimal places) for the following values of x. 5-x, (ii) 5.99 "PQ (iii) 5.999 PQ (v) 6.1 =3.030303 (iv) 5.9999 MpQ (vi) 6.01 = 3.003003 MpQ 13.333333 (vii) 6.001 MpQ = 2.727272 2.99999 (viii) 6.0001 2.970297 = 2.997003 1.99700 x X 5-x X (b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(6, -3). m=3 (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(6, -3). y = 3x - 21
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