`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^2-3x|+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^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 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^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]

L e tf(x)=x^3-x^2+12 x-3x=2,f(x)h a s 2ans1. Let f(x)=x-x+12x-3 thenx=2, f(x) has1) a maximum 2) a minimum3) both a maximum and a minimum4 neither a maximum nor a minimum

For any real number x ,l e t[x] denote the largest integer less than or equal to x ,L e tf be a real-valued function defined on the interval [-10 , 10] be f(x)={x-[x],if[x]i sod d1+[x]-x ,if[x]i se v e n Then the value of (pi^2)/(10)int_(-1)^(10)f(x)cospixdxi s____

Discuss the differentiability of f(x)={(x-e)2^(-2((1)/(e-x)))),x!= eat x=e and 0,x=e

f(x)=[(sinx)/x ,"w h e n"x!=0=2,"w h e n"x=0 sinx-, when x0/(x) =L= 2, when x=0

The function f(x)=x^(2)e^(-2x),x>0 .If l is maximum value of f(x) ,then find [l^(-1)] . (Where [.] represents greater integer function)

The function f(x)=x^2e^(-2x),x > 0. If l is maximum value of f(x) find [l^(-1)] (where [ ] denotes G.I.F.).