Page 348 - DMTH201_Basic Mathematics-1

Unit 13: Maxima and Minima

3
4. Find the nature of point of inffexion if y = 20 + 5x + 12x 2x , then x = Notes
2
(a) 2 (b) 3
(c) 4 (d) -2
4
5. Find minima if y = x 6x + 1
2
(a) 3 (b) 2

(c) 10 (d) 9

13.6 Review Questions

1. Fluid maxima/minima of the following functions, by using only first derivative.

(i) y x 2 10x 15 (ii) y x 3 3x 2 9x 20
4
(ii) y x 3 (x 2)
2. Find maxima, minima and point of inflexion, if any, of the following functions:

(i) y x 3 6x 2 12x 1 (ii) y 2x 3 3x 2 4

(iii) y x 4 4x 3 8x 2 (iv) y 3x 5 5x 3
(v) y x 4 2x 2 (vi) y x 2 / 3 x 1/ 3

x 2
(vii) y (viii) y x 4 4x 3 16x
x 2 1
1 4 2
(ix) y x 3 3x 2 5 (x) y x x 1
2
3. Find the absoute maxima/minima of the following functions:

(i) y 8x x 2 on [1, 5]
3
(ii) y x 7 on [–1, 3]
4

(iii) y 4 x 2 on [–2, 1]

(iv) 2 x on [–2, 2]
(v) 2 x on [4, 7]

1
(vi) y x 2 (4 x ) on [0, 3]
4. (a) If y x 4 4x 3 6x 2 4x 3 , show that y has a minimum at x = 1.

(b) If y x 5 5x 4 10x 3 10x 2 5x 10 , show that y has an inflexional value at
x = –1.
5. Find maxima, minima and the point of inflexion for the function y x 3 3x 2 9x 27 .
Show these points on a graph.
If the domain of the functions is [–2, 2], find maxima/minima.

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