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

Let f(x)=x^3+3x^2-9x+2 . Then, f(x) has a maximum at x=1 (b) a minimum at x=1 (c) neither a maximum nor a minimum at x=-3 (d) none of these

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

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)

Let f(x)=|x^2-3x-4|,-1lt=xlt=4 Then f(x) is monotonically increasing in [-1,3/2] f(x) monotonically decreasing in (3/2,4) the maximum value of f(x)i s(25)/4 the minimum value of f(x) is 0

let f(x)=(x^2-1)^n (x^2+x-1) then f(x) has local minimum at x=1 when

Let f (x)= int _(x^(2))^(x ^(3))(dt)/(ln t) for x gt 1 and g (x) = int _(1) ^(x) (2t ^(2) -lnt ) f(t) dt(x gt 1), then: (a) g is increasing on (1,oo) (b) g is decreasing on (1,oo) (c) g is increasing on (1,2) and decreasing on (2,oo) (d) g is decreasing on (1,2) and increasing on (2,oo)

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)

Let f(x)=(x-1)^(4) discuss the point at which f(x) assumes maximum or minimum value.

Let f(x)=x(x-1)^(2), find the point at which f(x) assumes maximum and minimum.

If f(x)=1+2x^2+4x^4+6x^6+....+100x^100 is a polynomial in real variable x , then f(x) has (a) neither a maximum nor a minimum (b) only one maximum (c) only one minimum (d) one maximum and one minimum