`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.

The interval in which y = x^(2) e^(–x) is increasing is

If f(x)=int_(x^(2))^(x^(2)+1)e^(-t^(2))dt , then find the interval in which f(x) increases.

Let f(x)={x+1,x >0 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).

If f(x)=int_(0)^(x)log_(0.5)((2t-8)/(t-2))dt , then the interval in which f(x) is increasing is

For all ' x^(prime),x^2+2a x+(10-3a)>0, then the interval in which ' a ' lies is

If f(x)={x^2,xlt=0 2sinx ,x >0'in v e s t iga t et h e function at x=0 for maxima/minima

Let f(x)=a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x , where a_i ' s are real and f(x)=0 has a positive root alpha_0dot Then f^(prime)(x)=0 has a positive root alpha_1 such that 0

Statement 1: If f(0)=0,f^(prime)(x)=ln(x+sqrt(1+x^2)), then f(x) is positive for all x in R_0dot Statement 2: f(x) is increasing for x >0 and decreasing for x<0

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___

Find the intervals in which the function f given by f(x) = 2x^(2) – 3x is (a) increasing (b) decreasing