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The function f(x)""=""t a n^(-1)(sinx""+...

The function `f(x)""=""t a n^(-1)(sinx""+""cosx)` is an increasing function in (1) `(pi/4,pi/2)` (2) `(-pi/2,pi/4)` (3) `(0,pi/2)` (4) `(-pi/2,pi/2)`

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The function f(x)=tan^(-1)(sin x+cos x) is an increasing function in (-(pi)/(2),(pi)/(4))(b)(0,(pi)/(2))(-(pi)/(2),(pi)/(2))(d)((pi)/(4),(pi)/(2))

Prove the following f(x)=tan^(-1)(sinx+cosx) is strictly decreasing function on ((pi)/(4),(pi)/(2)) .

Show that the function f(x)=cot^(-1)(sin x+cos x) is decreasing on (0,pi/4) and increasing on (pi/4,pi/2)

Show that f(x)=cos(2x+pi/4) is an increasing function on (3 pi/8,7 pi/8)

Show that f(x)=cos(2x+(pi)/(4)) is an increasing function on (3 pi/8,7 pi/8)

The largest interval lying in (-pi/2,pi/2) for which the function [f(x)=4^-x^2+cos^(-1)(x/2-1)+log(cosx)] is defined, is (1) [0,pi] (2) (-pi/2,pi/2) (3) [-pi/4,pi/2) (4) [0,pi/2)

If cos(sinx)=0, then x lies in (a) (pi/4,pi/2)uu(pi/2,\ pi) (b) (-pi/4,\ 0) (c) (pi,(3pi)/2) (d) null set

The range of function f(x)=cot^(-1)x+sec^(-1)x+ cosec^(-1)x is (A) [(pi)/(2), pi)uu(pi, (3 pi)/(2)] (B) ((pi)/(2), (3 pi)/(4)] uu [(5 pi)/(4), (3 pi)/(2)) (C) ((pi)/(2), pi)uu(pi ,(3 pi)/(2)) (D) ((pi)/(2), (3 pi)/(2))

f:R rarr R , f(x)=tan^(-1)(2^x) + k is an odd function, then k= (A) -pi/4 (B) (pi)/(4) (C) -(pi)/(2) (D) (pi)/(2)

show that the function f(x)=sin x is strictly increasing in (0,(pi)/(2)) strictly decreasing in ((pi)/(2),pi)

JEE MAINS PREVIOUS YEAR-APPLICATION OF DERIVATIVES-All Questions
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  5. Suppose the cube x^3""p x""+""q has three distinct real roots wh...

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  14. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

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  16. The normal to the curve, x^2+""2x y-3y^2=""0,""a t""(1,""1) : (1) ...

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  17. Consider f(x)=tan^(-1)(sqrt((1+sinx)/(1-sinx))), x in (0,pi/2)dot A n...

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  18. A wire of length 2 units is cut into two parts which are bent respe...

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