Find the maximum and minimum values, if any, of the following functions
given by
(i) f (x) = |x + 2| – 1
(ii) g(x) = – |x + 1| + 3
(iii) h(x) = sin(2x) + 5
(iv) f (x) = |sin 4x + 3|
(v) h(x) = x + 1, x ∈ (– 1, 1)
3 Find the local maxima and local minima, if any, of the following functions Find
also the local maximum and the local minimum values, as the case may be:
(i) f (x) = x2
(ii) g(x) = x3 – 3x
(iii) h(x) = sin x + cos x, 0
2
x
π
<
<
(iv) f (x) = sin x – cos x, 0
2
<x
< π
(v) f (x) = x3 – 6x2 + 9x + 15
(vi)
2
( )
,
0
x2
g x
x
x
=
+
>
(vii)
2
1
( )
2
g x
x
=
+
(viii)
( )
1
, 0
1
=
−
<
<
f x
x
x
x
4 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