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How can we find range of (tanx) 2 + tanx using monotonicity.

How can we find range of (tanx)2 + tanx using monotonicity.

Grade:12

1 Answers

Aditya Gupta
2081 Points
5 years ago
hello khushi. we know that the range of tanx is R.
so keep y=tanx
so now we have to find range of (tanx)2 + tanx= y^2+y
now, when y= ± infinity, y^2+y is + infinity.
now differentiate y^2+y wrt y and equate it to zero to find minimum value.
2y+1=0
or y = – ½ 
so min value is ¼ – ½ 
= – ¼ 
hence the range is [ – ¼, infinity)

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