`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^2+3x ,-1lt=x<0-sinx ,0lt=x

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 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+2,x<-1x^2,-1lt=x<1(x-2)^2,xgeq1 Then number of times f^(prime)(x) changes its sign in (-oo,oo) is___

L e tf(x)={x+2 , x <-1 ; x^2 , -1 lt= x < 1 and (x-2)^2 , x geq 1 Then number of times f^(prime)(x) changes its sign in (-oo,oo) is___

L e tf(x)={x+2 , x <-1 ; x^2 , -1 lt= x < 1 and (x-2)^2 , x geq 1 Then number of times f^(prime)(x) changes its sign in (-oo,oo) is___

L e tf(x)={x+2 , x <-1 ; x^2 , -1 lt= x < 1 and (x-2)^2 , x geq 1 Then number of times f^(prime)(x) changes its sign in (-oo,oo) is___

L e tf(x)={(|x^3+x^2+3x+sinx|(3+sin(1/x)) ,, x!=0), (0 ,, x=0):} then the number of point where f(x) attains its minimum value is_____

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