Let `f(x)=x^4-4x^3+6x^2-4x+1.` Then, (a) `f` increase on `[1,oo]` (b) `f` decreases on `[1,oo]` (c)`f` has a minimum at `x=1` (d)`f` has neither maximum nor minimum

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) = 2/3 x^3-6x^2+20x-5 has neither a maximum nor a minimum value.

If f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x) then f(x) (a)increase in (0,oo) (b)decrease in [0,oo] (c)neither increases nor decreases in [0,oo] (d)increase in (-oo,oo)

Show that, f(x) =sinx-(x^(3))/(3!)-(x^(5))/(5!) is neither maximum nor minimum at x=0.

If f(x)=xe^(x(1-x)) , then f(x) is(a) increasing on [−1/2,1] (b) decreasing on R (c) increasing on R (d) decreasing on [−1/2,1]

f has a local maximum at x = a and local minimum at x = b. Then -

Consider the function f:(-oo,oo)to(-oo,oo) defined by f(x)=(x^2-a)/(x^2+a),a >0, which of the following is not true?(a) maximum value of f is not attained even though f is bounded. (b) f(x) is increasing on (0,oo) and has minimum at x=0 (c) f(x) is decreasing on (-oo,0) and has minimum at x=0. (d) f(x) is increasing on (-oo,oo) and has neither a local maximum nor a local minimum at x=0.

If f(x)=x^3-4x+1 , then find f(0) .

Let f(x)=(x)/(1+|x|) Interval of increase of f(x) is -

Let f be the function f(x)=cosx-(1-(x^2)/2)dot Then (a) f(x) is an increasing function in (0,oo) (b) f(x) is a decreasing function in (-oo,oo) (c) f(x) is an increasing function in (-oo,oo) (d) f(x) is a decreasing function in (-oo,0)