If `f(x)=x^(3)+ax^(2)+ax+x(tantheta+cottheta)` is increasing for all x and if `thetain(pi,(3pi)/(2))` then -

If f(x)= x^(3) + ax^(2) + bx + c is an increasing function for all real values of x then-

If f(x) =x^(3) +ax^(2)+bx +5 sin^(2) x is an increasing function on R, then

Show that f(x) = x^(3) + 3ax^(2) + 3a^(2) + b is increasing on R for all values of a and b.

If f(x)=x^(3)+ax^(2)+bx+5sin^(2)x, AA x in R is an increasing function, then …………..

If y = x^3 - ax^2 + 48x + 7 is an increasing function for all real values of x, then a lies in

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)]

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)]

Consider f(x)=sin3x,0<=x<=(pi)/(2), then (a) f(x) is increasing for x in(0,(pi)/(6)) and decreasing for x in((pi)/(6),(pi)/(2)) (b) f(x) is increasing forx in(0,(pi)/(4)) and decreasing for x in((pi)/(4),(pi)/(2)) (c) f(x)

Let f(x)=x^(3)+ax^(2)+bx+5 sin^(2)x be an increasing function on the set R. Then,

condition that f(x)=x^(3)+ax^(2)+bx^(2)+c is anincreasing function for all real values of x' is