Show that the function f(x) `=sin^(4)x+cos^(4)x` is increasing in `(pi)/(4) lt x lt (3pi)/(8)`.

The function f(x)=sin^4x+cos^4x increasing if :

Show that, the function f(x)=cos 2x is increasing at x=(3pi)/4 .

Verify the truth of Rolle's theorem for the functions: f(x)=cos^(2)x" in " -(pi)/(4) le x le (pi)/(4)

Differentiate w.r.t.x the function in Exercises 1 to 11. (sin x- cos x)^( sin x - cos x), (pi)/(4) lt x lt (3pi)/(4) .

Prove that, the function 5+24x+3x^(2)-x^(3) increases in the interval -2 lt x lt 4 .

Consider the function f(x) = (x^(3))/(4) - sin pi x + 3

Find the range of the function f(x) = (sec^2x - tan x)/(sec^2 x + tan x) , (-pi/2 lt x lt pi/2) .

Prove that the function f given by f (x) = log cos x is decreasing on (0,(pi)/(2)) and increasing on ((3pi)/(2) ,2pi) .

Consider the function f(x) = sin^(-1)x , having principal value branch [(pi)/(2), (3pi)/(2)] and g(x) = cos^(-1)x , having principal value brach [0, pi] For sin^(-1) x lt (3pi)/(4) , solution set of x is

Let f(x)=sin^(4)x-cos^(4)x int_(0)^((pi)/(2))f(x)dx =