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Question

y=x(x-3)2 decreases for the values of x given by:


A

1<x<3

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B

x<0

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C

x>0

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D

0<x<3/2

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Solution

The correct option is A

1<x<3


Explanation for the correct option:

Option (A): Given that y=x(x-3)2

Graphical representation of y=x(x-3)2 is as follows:

From the graph it is clear that the curve of y=x(x-3)2 decreases in the interval1<x<3

Hence, Option (A) is correct.

Explanation for the incorrect options:

Option (B) From the graph it is clear that the curve of y=x(x-3)2 increases in the interval x<0

Option (C) From the graph it is clear that the curve of y=x(x-3)2 increases in the interval x<1 and then decreases in the interval 1<x<3. and again increases in the interval 3<x Hence y=x(x-3)2 does not decrease for all values of x in the interval x>0.

Option (D) From the graph it is clear that the curve of y=x(x-3)2 increases in the interval 0<x<1 and then decreases in the interval 1<x<32. Hence y=x(x-3)2 does not decrease for all values of xin the interval 0<x<32.

Therefore, option (B), (C) and (D) are incorrect.

Hence the correct option is Option (A).


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