ThepointP(7,-4)liesonthecurvey=4/(6-x)(a)IfQisthepoint(x,4/6-x),useyourcalculatortofindtheslopemPQofthesecantlinePQ(correcttosixdecimalplaces)forthefollowingvaluesofx.(1)6.9mPQ=?(2)6.99mPQ=?(3)6.999mPQ=?(4)6.99

Question

The point P(7,-4)lies on the curve y=4/(6-x)
(a) If Q is the point(x,4/6-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.
(1) 6.9 mPQ=?
(2) 6.99 mPQ=?
(3) 6.999 mPQ=?
(4) 6.9999 mPQ=?
(5) 7.1 mPQ=?
(6) 7.01 mPQ=?
(7) 7.001 mPQ=?
(8) 7.0001 mPQ=?
(b) Using the results of part (a),guess the value of the slope m of the tangent line to the curve at P(7,-4),m=?
(c) Using the slope from part (b),find an equation of the tangent line to the curve at P(7,-4)

Answer 1

a):
题目的意思是求割先PQ的斜率,P点坐标已知,Q点坐标取不同的给定值,P,Q都在双曲线上.
b):由1--8的过程猜测P点的切线斜率；
c):由b,写出P点的斜率公式.
教材中的内容,不难,你自己慢慢算一下.按步骤来.