`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,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^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_____

If f(x)=max{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), 0 lt= x lt = 1/4 x^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 f (x)= {{:(x ^(2),0lt x lt2),(2x-3, 2 le x lt3),(x+2, x ge3):} then the tuue equations:

if f(x)= {x^3+x^2,for 0lt=xlt=2x+2 ,for2

The relation f is defined by f(x)={x^2,0lt=xlt=3 3x ,3lt=xlt=10 The relation g is defined by g(x)={x^2,0lt=xlt=3 3x ,2lt=xlt=10 Show that f is a function and g is not a function.

The relation f is defined by f(x)={x^2,0lt=xlt=3 3x ,3lt=xlt=10 The relating g is defined by g(x)={x^2,0lt=xlt=3 3x ,2lt=xlt=10 Show that f is a function and g is not a function.

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____

Evaluate the following integral: int_0^9f(x)dx ,\ w h e r e\ f(x)=sinx,\ 0lt=xlt=pi//2 w h e r e\ f(x)= 1 ,pi/2lt=xlt=3 w h e r e\ f(x)=e^(x-3),\ 3lt=xlt=9