`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.

Let f(x)={1+(2x)/a ,0lt=x<1 and ax ,1lt=x<2 If lim_(x->1)f(x) exists ,then a is (a) 1 (b) -1 (c) 2 (d) -2

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___

If f(x)=m a xi mu m{x^3, x^2,1/(64)}AAx in [0,oo),t h e n f(x)={x^2,0lt=xlt=1x^3,x >0 f(x)={1/(64),0lt=xlt=1/4x^2,1/4 1 f(x)={1/(64),0lt=xlt=1/8x^2,1/8 1 f(x)={1/(64),0lt=xlt=1/8x^3,x >1/8

Let the function f(x be defined as follows: f(x)={x^3+x^2-10 x ,-1lt=x<0cosx ,0lt=x

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_____

The number of points of discontinuity of g(x)=f(f(x)) where f(x) is defined as, f(x)={1+x ,0lt=xlt=2 3-x ,2 2

L e tf(x)=x^3-(3x^2)/2+x+1/4 Then the value of (int_(1/4)^(3/4)f(f(x))dx)^(-1) is____

Find the mean and variance of the distribution f(x) = {(3e""^(-3x),0lt xltoo),(0,"elsewhere"):}