`L e tf(x)={x^2+3x ,-1lt=x<0-sinx ,0lt=x

L e tf(x)={|x^2-3x|+a ,0lt=x<3/2-2x+3,xgeq3/2 If f(x) has a local maxima at x=3/2 , then greatest value of |4a| is _________

L e tf(x)={x e^(a x),xlt=0x+a x^2-x^3,x >0 where a is a positive constant. Find the interval in which f^(prime)(x) is increasing.

L e tf(x)={x^3+x^2+3x+sinx|(3+s in1/x ,),x!=0. 0x=0 then the number of point where f(x) attains its minimum value is_____

L e tf(x)=x^3-x^2+12 x-3x=2,f(x)h a s 2ans1. Let f(x)=x-x+12x-3 thenx=2, f(x) has1) a maximum 2) a minimum3) both a maximum and a minimum4 neither a maximum nor a minimum

L e tf(x)={(x^4-5x^2+4)/(|(x-1)(x-2)6),x!=1,2 12,x=2x=1 then f(x) is continuous on the set R (b) R-[1] (c) R-[2] (d) R-[1,2]

The p.d.f. of a continuous r.v. X is f(x)={{:((x^(2))/(3)","-1lt x lt 2),(0", otherwise"):} , then P(1 lt X lt2) =

f(x) is defined as f(x) = {{:(|x|+[x],-1lt x lt 1,),(x+|x|,1 le x lt 2,),(|x|[x],2 le x lt 3,):} then the number of points of dicontinuity of f(x) is

The total number of local maxima and local minima of the function f(x) = {{:( (2 + x)^(3) "," , -3 lt x le -1) , (x^(2//3) "," , -1 lt x lt 2):} is