1. Find the turning points of each of the following functions and determine their nature by examining the gradient on each side of the turning point.
|
a
|
f(x) = 6x − x2 |
b
|
f(x) = 8x + x2 |
c
|
y = x3 |
|
d
|
y = 1 − 3x + 3x2 − x3 |
e
|
g(x) = x3 − 12x |
f
|
y = 27x − x3 |
|
g
|
f(x) = √(9 − x2) |
h
|
y =  |
i
|
f(x) = |
|
j
|
f(x) =  |
k
|
y = 192x − 88x2 + 16x3 − x4 |
l
|
y = (x − 3)4 |
|
m
|
f(x) = (x + 2)3 |
n
|
g(x) = x4 − 8x3 + 18x2 |
o
|
y = x(x − 6)2 |
2. Find the turning points of each of the following functions and determine their nature by using the second derivative test.
|
a
|
f(x) = 8x − x2 |
b
|
y = 5x + x2 |
c
|
g(x) = x3 + 3x2 − 105x |
|
d
|
y = 48x − x3 |
e
|
y = x3 − 27x + 1 |
f
|
f(x) = 12x2 − x3 |
|
g
|
y = 12x − x3 |
h
|
f(x) = 6x2 − 2x3 |
i
|
g(x) = x3 + 3x2 + 3x + 1 |
|
j
|
f(x) = x4 |
k
|
y = x4 − 2x3 |
l
|
f(x) = ex |
|
m
|
y = x(x2 + 3) |
n
|
f(x) = 4x3 − x5 |
o
|
y = x4 + 4x3 − 2x2 − 12x |
