The function `f(x)=sin^4x+cos^4x` increasing in interval

The function f(x)=x^(1//x) is increasing in the interval

State when a function f(x) is said to be increasing on an interval [a , b]dot Test whether the function f(x)=x^2-6x+3 is increasing on the interval [4,6]dot

State when a function f(x) is said to be increasing on an interval [a ,\ b] . Test whether the function f(x)=x^2-6x+3 is increasing on the interval [4,\ 6] .

The function f(x) = sin ^(4)x+ cos ^(4)x increases, if

Show that the function f(x)=sin^(4) x+ cos^(4) x (i) is decreasing in the interval [0,pi/4] . (ii) is increasing in the interval [pi/4,pi/2] .

The function f(x)=(sin^4x+cos^4x)/(x+tanx) is :

Separate the interval [0,pi/2] into sub intervals in which function f(x)=sin^4(x)+cos^4(x) is strictly increasing or decreasing.

The function f(x)=x^2-x+1 is increasing and decreasing in the intervals

which of the following statement is // are true ? (i) f(x) =sin x is increasing in interval [(-pi)/(2),(pi)/(2)] (ii) f(x) = sin x is increasing at all point of the interval [(-pi)/(2),(pi)/(2)] (3) f(x) = sin x is increasing in interval ((-pi)/(2),(pi)/(2)) UU ((3pi)/(2),(5pi)/(2)) (4) f(x)=sin x is increasing at all point of the interval ((-pi)/(2),(pi)/(2)) UU ((3pi)/(2),(5pi)/(2)) (5) f(x) = sin x is increasing in intervals [(-pi)/(2),(pi)/(2)]& [(3pi)/(2),(5pi)/(2)]

Find the intervals in which the function f(x)=x^4-(x^3)/3 is increasing or decreasing.