Find the slope of the secant to the curve f(x) = -2logx + 3 between: (1 each)

Question

i) x = 1 and x = 2

ii) x = 1 and x = 1.5

iii) x = 1 and x = 1.1

vi) x = 1 and x = 1.01

b) Extend the result from part a to determine the slope of the tangent to the curve at x = 1 accurate to 3 decimal places. (2 marks)

Answer 1

i) f(1) = -2log(1) + 3 = 3
f(2) = -2log2 + 3

slope of secant = (-2log2 + 3 - 3)/1 = -2log2
= appr -.602

....

iii) f(1) = 3
f(1.1) = -2log 1.1 + 3
slope = (-2log 1.1 + 3 - 3)/(1.1-1) = -2log 1.1 /.1
= appr -.828

iv)
...
slope = -2log1.01 /.01
= appr -.864

etc.