`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.

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

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_____

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

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^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]

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

The p. d. f. of a continuous r. v. Xis f(x) = {:((3x^2)/8 , 0 lt x lt 2),(0, "otherwise"):} Determine the c.d.f of X and hence find (i) P(X lt 1), (ii) P(1 lt X lt 2) .

Number of points where f (x)= {{:(max(|x ^(2)- x-2","x ^(2) -3x),,, x ge0),( max (ln (-x)"," e ^(x)),,, x lt 0):} is non-differentiable will be:

If f(x) ={(4-3x,",",0 lt x le 2),(2x-6,",",2 lt x le 3),(x+5,",",3 lt x le 6):} , then f(x) is