`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^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|+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|+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 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 <-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+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___