Page 374 - DMTH201_Basic Mathematics-1

Unit 14: Business Applications of Maxima and Minima

(c) increasing in (0, p/4) and decreasing in (p/4, p/2) Notes
(d) none of these
3. Let f (x) = (4–x ) , then f has a
2 2/3
(a) a local maxima at x = 0

(b) a local maxima at x = 2
(c) a local maxima at x = –2
(d) none of these
4. Let f (x) = x – 6x + 9x + 18, then f (x) is strictly decreasing in
3
2
(a) (– , 1]
(b) [3, )
(c) (– , 1] [3, )
(d) [1, 3]

5. The absolute minimum value of x – x – 2x+ 5
2
4
(a) is equal to 5
(b) is equal to 3
(c) is equal to 7

(d) does not exist
6. Equation of the tangent to the curve y = e –|x| at the point where it cuts the line x=1
(a) is ey + x =2
(b) is x + y = e

(c) is ex + y = 1
(d) does not exist
7. Rolle’s theorem holds for the function x + bx + cx, 1 < x < 2 at the point 4/3, the value of
2
3
b and c are;
(a) b = 8, c = - 5
(b) b = -5, c = 8
(c) b = 5, c = -8

(d) b = -5, c = -8.
8. The number of value of k for which the equation x – 3x + k = 0 has two different roots lying
3
in the interval (0, 1) are
(a) 3
(b) 2
(c) infinitely many
(d) no value of k satisfies the requirement.

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