The domain of the funciton `f(x)` given by `3^(x) + 3^(f) = "min" (2t^(3) - 15t^(2) + 36+ - 25, 2 + |sin t| , 2 le t le 4)` is

Let the function y = f(x) be given by x= t^(5) -5t^(3) -20t +7 and y= 4t^(3) -3t^(2) -18t + 3 where t in ( -2,2) then f'(x) at t = 1 is

The position of a particle moving in a string line is given by x = 3t^(3) - 18 t^(2) + 36 t Here, x is in m and t in second . Then

The function f(t) = 4 sin^(3) t -6 sin^(2) t +12 sin t + 100 is strictly :

The position of a particle moving in a straight line is given by x=3t^(3)-18t^(2)+36t Here, x is in m and t in second. Then

Let f : [ 0, oo) to [ 0,3] be a function defined by f(x) = {{:(max { sin t : 0 le t le x}" , " 0 le x le pi),( 2 + cos x", " x gt pi ):} Then which of the following is true ?

A function f(x) satisfies f(x)=sin x+int_(0)^(x)f'(t)(2sin t-sin^(2)t)dt is

Each of the four particles move along an x axis. Their coordinates (in metres) as function of time (in seconds) are given by Particle 1 : x(t) = 3.5 - 2.7 t^3 Particle 2 : x(t) = 3.5 + 2.7 t^3 Particle 3 : x(t) = 3.5 + 2.7 t^2 Particle 4 : x(t) = 2.5 - 3.4t - 2.7 t^2 which of these particles is speeding up for t > 0?