Page 36 - Engineering Mathematics Workbook_Final

Calculus


local minima x = 4 and point of 0 x  5. Then F has local minimum at
inflection at x = 1 are the points

(a) 3, 24 (b) -3, -24 (a) {0,2,4} (b) {1,3,5}

(c) -3, 24 (d) 0, 0 (c) {0,3,4} (d) {3,4,5}

[JAM CA 2005] [JAM CA 2007]

190. The value of x and x with x  x 193. Consider the function
1 2 1 2 2
x

2
such that (12 − x − x 2 ) dx has the f ( ,x y ) (x= + ) y − (x + y ) 1+ .
x 1 The absolute maxima value and the
largest value are absolute minimum value of the function

(a) -3, 3 (b) -4, 1 on the unit square.

x
(c) -4,4 (d) -4,3 (  , x y ):0   1,0  y   1 ,

[JAM CA 2005] respectively are

f x =
+
191. For ( ) (1 sin x )cos x , where (a) 3 and 3 (b) 3 and 3
0  x  2p , where of the following 2 2 4
statements is true 3 3
(c) 3 and (d) 2 and
 4 4
f
(a) ( ) x has a local maxima at x =
6 [JAM CA 2007]

(b) ( ) x has a local minima at x = 194. Let ( ) x = x − x + 1, 0 x  1.

2
3
f
f
3
Then the absolute minima value of
f
(c) ( ) x has a local maxima at f ( ) x is
5
x = 14 5
3 (a) (b)
27 9
3
(d) ( ) x has a local minima at x = 23
f
4 (c) (d) 1
27
[JAM CA 2006] x
2
F
195. Let ( ) x =  (t − 3t + ) 2 dt . Then

0
192. Let F has
f ( ) x =  x (t − 1 )(t − 2 )(t − 3 )(t − ) 4 dt , (a) a local maximum at x = 1 and a local
0 minimum at x = 2

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