Statement 1: `f(x)=(x^3)/3+(a x^2)/2` + x+5 has positive point of maxima for `a<-2.` Statement 2: `x^2+a x+1=0` has both roots positive for `a<2.`

Column I Column II f(x)=x^2logx f(x) has one point of minima f(x)=x(log)_e x q. f(x) has one point of maxima f(x)=(logx)/x r. f(x) increase x in (0,e) f(x)=x^(-x) s. f(x) decrease x in (0,1/e)

Statement 1: f(x)=|x-1|+|x-2|+|x-3| has point of minima at x=3. Statement 2: f(x) is non-differentiable at x=3.

Statement 1: The function f(x)=x^4-8x^3+22 x^2-24 x+21 is decreasing for every x in (-oo,1)uu(2,3) Statement 2: f(x) is increasing for x in (1,2)uu(3,oo) and has no point of inflection.

The function f(x)=x^(1/3)(x-1) has two inflection points has one point of extremum is non-differentiable has range [-3x2^(-8/3),oo)

Discuss the extremum of the function f(x)=(x-1)(x-2)(x-3).How many criticla points f(x) has?

Consider the graph of the function f(x) = x+ sqrt|x| Statement-1: The graph of y=f(x) has only one critical point Statement-2: fprime (x) vanishes only at one point

If f(x)=x^(2)-3x , then the points at which f(x)=f'(x) are

If f(x)=x^(2)-3x , then the points at which f(x) = f'(x) are :

The curve f(x)=(x^2+a x+6)/(x-10) has a stationary point at (4,1) . Find the values of aa n db . Also, show that f(x) has point of maxima at this point.