Iff{x} denotes the smallest integer greater than or equal to x, what is the positive difference between the maximum and minimum value ofy x f{x] such that:-3.2 x 3.2 andy = {y, y E integers, -y- 15}a)0b)14c)98d)12Correct answer is option 'D'. Can you explain this answer?

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Iff{x} denotes the smallest integer greater than or equal to x, what is the positive difference between the maximum and minimum value ofy x f{x] such that:-3.2 < x < 3.2 andy = {y, y E integers, |y| < 15}

a)
0
b)
14
c)
98
d)
12

Correct answer is option 'D'. Can you explain this answer?

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Iff{x} denotes the smallest integer greater than or equal to x, what i...

The maximum value off{x) as well as y is positive.

So, y x f{x) takes its maximum value when both f{x) and y are maximum.

Maximum value ofy x f{x} = 14 x/{3.2} = 14 x 4 = 56

The minimum value off{x] as well as y is negative.

Hence, if both of them are considered for minimum value ofy x f{x], the product becomes positive (which is not minimum).

Hence, consider the minimum value of one and the maximum value of the other variable to get the minimum product (as their signs will be negative).

Minimum value ofy x f{x} = -14 x/{3.2} = -14 x 4 = -56

Hence, option 4.

Note: If you takey = 14 (maximum) and/{-3.2} = -3 (i.e. minimum), the product becomes -42. This is not the minimum value of the product, as seen above.

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Iff{x} denotes the smallest integer greater than or equal to x, what is the positive difference between the maximum and minimum value ofy x f{x] such that:-3.2 x 3.2 andy = {y, y E integers, |y| 15}a)0b)14c)98d)12Correct answer is option 'D'. Can you explain this answer?

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