I wrote the answers to part A. I need help with part B and C only! The point P(5
ID: 3139193 • Letter: I
Question
I wrote the answers to part A. I need help with part B and C only!
The point
P(5, ?2)
lies on the curve
y = 2/(4 ? x).
(a) If Q is the point
(x, 2/(4 ? 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) 4.9
mPQ =
(ii) 4.99
mPQ =
(iii) 4.999
mPQ =
(iv) 4.9999
mPQ =
(v) 5.1
mPQ =
(vi) 5.01
mPQ =
(vii) 5.001
mPQ =
(viii) 5.0001
mPQ =
(b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at
P(5, ?2).
m =
(c) Using the slope from part (b), find an equation of the tangent line to the curve at
P(5, ?2).
Explanation / Answer
slope of line (x1,y1) and (5,-2) y-y1 = (-2-y1)/(5-x1) x (x-x1) slope is -(2+y1)/(5-x1) where y1 = 2/(4-x1) 1) x1=4.9 mPQ= 2.2222222222 2)x1=4.99 mPQ= 2.020202 3)4.999 mPQ= 2.002002002 4)x1= 4.9999 mPQ= 2.00020002 5)x1=5.1 mPQ=1.818181 6) mPQ = 1.98019802 7)mPQ= 1.998001998 8)mPQ =1.99980002 b) y=2/4-x dy/dx = -2/(4-x)^2 at (5,-2) slope = -1 c) y+2 = -1(x-5) x+y =3