Let f (x)=sin x –tan x, x∈(0,π2), then tangent drawn to the curve in the given interval will lie;
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a
above the curve
b
below the curve
c
nothing can be said
d
none of thee
answer is A.
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Detailed Solution
f (x) = sin x –tan x ⇒f '(x) = cos x –sec2x ⇒f ''(x) = −sin x –2 sec2x. tan x =−(sinx+2sinxcos3x) =[−] ve for x∈R(0, π2) ⇒ Tangent drawn to the curve will lie above the curve.