University of South Africa MAT1613 Exam
questions and answers best solved latest
update 2022
Memorandum Nov2017 MAT1613
paper a) f (x) = ln(2x + 1) − 3x , x > 0
2 −3
fJ(x) =
2x + 1
2 − 3(2x + 1)
=
2x + 1
−1 − 6x
=
2x + 1
y = —6x − 1 + + + −-
-
y = 2x + 1 - + + +
Sign x=0
f (x)
J — + + −
pattern: +
-1/2 -1/6
-
i) Since we are only looking at values > 0 , f decreases on (0, ∞)
ii) f J (x) = 0 when −1−6x 6 1 but
2x+1 = 0 i.e.when x = − 6 - 1 < 0 so no extreme value.
b)
−6( 2x + 1) + 2(6x + 1)
fJJ(x) =
(2x + 1)2
University of South Africa MAT1613 Exam
questions and answers best solved latest
update 2022
questions and answers best solved latest
update 2022
Memorandum Nov2017 MAT1613
paper a) f (x) = ln(2x + 1) − 3x , x > 0
2 −3
fJ(x) =
2x + 1
2 − 3(2x + 1)
=
2x + 1
−1 − 6x
=
2x + 1
y = —6x − 1 + + + −-
-
y = 2x + 1 - + + +
Sign x=0
f (x)
J — + + −
pattern: +
-1/2 -1/6
-
i) Since we are only looking at values > 0 , f decreases on (0, ∞)
ii) f J (x) = 0 when −1−6x 6 1 but
2x+1 = 0 i.e.when x = − 6 - 1 < 0 so no extreme value.
b)
−6( 2x + 1) + 2(6x + 1)
fJJ(x) =
(2x + 1)2
University of South Africa MAT1613 Exam
questions and answers best solved latest
update 2022
