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.`

Show that the function f(x)=(2)/(3)x^(3)-6x^(2)+20x-5 has neither a maximum nor a minimum value.

The function f(x)= 2x^(3) - 3x^(2) - 12x +4 has-

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.

Show that the function f(x) = 2/3 x^3-6x^2+20x-5 has neither a maximum nor a minimum value.

Show that the function f(x)=4x^3-18x^2+27x-7 has neither local maxima and local minima

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.

Statement 1: Minimum number of points of discontinuity of the function f(x)=(g(x)[2x-1]AAx in (-3,-1) , where [.] denotes the greatest integer function. and g(x)=a x^3+x^2+1 is zero. Statement 2: f(x) can be continuous at a point of discontinuity, say x=c_1 of [2x-1] if g(c_1)=0. which statement is true?

Find the points at which the function f given by f(x)=(x-2)^4(x+1)^3 has local maxima local minima point of inflexion

Let f(x)=2x^3-9x^2+12 x+6. Discuss the global maxima and minima of f(x)

The function f(x)=x^(1/3)(x-1) has two inflection points, has one point of extremum, is non-differentiable, has range [-3*2^(-8/3),oo)