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Question

The arrangment of the slopes of the normals to the curve y=elog(cosx) in the ascending order at the points given below.
A)x=π6,B)x=7π4,C)x=11π6,D)x=π3

A
C,B,D,A
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B
B,C,A,D
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C
A,D,C,B
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D
D,A,C,B
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Solution

The correct option is C C,B,D,A
We have, y=elogcosx=(cosx)loge[alogbc=clogba]=cosx
dydx=sinx=m(say)
Thus slope of normal to the given curve at any point is,
m=1m=1sinx
Now, mπ6=2,m7π4=2,mπ6=2,mπ6=32
Clearly ascending order is, C,B,D,A
Note: Given function is not defined where cosx<0

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