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Question

If slope of tangent at atleast one point to the curve y=x3+3ax2+3x+7 is negative, then

A
a(,0)
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B
a(,1)
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C
a(1,1)
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D
a(1,)
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Solution

The correct option is D a(1,)
Given curve: y=x3+3ax2+3x+7
Differentiating both sides w.r.t. x
y=3x2+6ax+3
Since, y<0 (for atleast one point)
3x2+6ax+3<0
D>0
36a236>0
a(,1) (1,)

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