Prove that the following  functions do not have maxima or minima:
(i) f (x) = ex
(ii) g(x) = log x
(iii) h (x) = x3 + x2 + x +1
5 Find the absolute maximum value and the absolute minimum value of the following
functions in the given intervals:
(i) f (x) = x3, x ∈ [– 2, 2]
(ii) f (x) = sin x + cos x , x ∈ [0, π]
(iii) f (x) =
12
9
4
,
2,
2
2
x
x
x


−
∈ −




(iv)
2
( )
(
1)
3,
[ 3,1]
f x
x
x
=
−
+
∈ −
6 Find the maximum profit that a company can make, if the profit function is
given by
p(x) = 41 – 72x – 18x2
7 Find both the maximum value and the minimum value of
3x4 – 8x3 + 12x2  – 48x + 25 on the interval [0, 3]