Page 160 - DECO403_MATHEMATICS_FOR_ECONOMISTS_ENGLISH

Unit 9: Maxima and Minima: One Variable

Self Assessment Note
2. State whether the following statements are True or False:

2
dy
5. At x = a for maximum, the value of is positive.
dx 2
2
dy
6. At x = a for minimum, the value of is negative.
dx 2
7. There will be a certain maximum or minimum value between the two equal values of
function.
dy
8. At the maximum or minimum point of function the sign of changes.
dx

9.6 Summary

z If the height of your house is more than the houses situated in neighbourhood (right or left),
then the height of your house will be called maximum and contrary to this if the height is
less, then it will be called Minimum.
z Function decreases to some certain point of independent variable and grows towards the
next values, then arriving from the state of decreasing to an increasing state, the function
obtains minimum value.

z Maximum value comes after minimum value and minimum comes after maximum viz
maximum and minimum comes in a sequence.
2
dy
z If for any value of x value of 2 is positive, then function for that value of x is minimum and
dx
if it is negative, then value would be maximum.

9.7 Keywords

z Maximum: more value
z Minimum: less value

9.8 Review Questions

1. Find out the maximum and minimum value of x – 2x +x + 6
3
2
166
[Ans.: Maximum , Minimum = 6]
27
2
2. Find out the maximum value of function (x – 1) (x – 2) (x – 3). [Ans.: Maximum ]
33
x
1
§·
3. Prove that the maximum value of ¨¸ is (e) 1/e
x
©¹
3
4. At what values of x, function 2x – 9x + 12x – 3, x is maximum or minimum
2
[Ans.: Maximum = 2, Minimum = 1]

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