`f(x)=int_0^x e^-t^2(t-5)(t^2-7t+12)dt` for all `x in (0,oo)` then (A) f has local maximum at x=4 and a local minimum at x=3 (B) f is decreasing on `(3,4)uu(5,oo)` and inccreasing on `(0,3)uu(4,5)` (C) There exists atleats two `c_1,c_2 in (0,oo)` such that `f''(c_1)=0` and `f''(c_2)=0` (D) There exists some `c in (0,oo)` such that `f'''(c)=0`

Let f(x)=int_0^xe^(-t^2)(t-5) (t^2-7t+12) dt for all x in (0, oo) then (A) f has a local maximum at x = 4 and a local minimum at x=3 (B) f is decreasing on (3,4)(5, oo) and increasing on (0,3) (4,5). (C) There exists atleast two c_1, c_2 in (0, oo) such that f"(c_1)=0 and f"(c_2)=0. (D) There exists some c in (0, oo) such that f"'(c) = 0

If f(x)=int_(0)^(x)e^(t^(2))(t-2)(t-3)dt for all x in(0,oo) , then

If f(x) = int_(0)^(x) e^(t^(2)) (t-2) (t-3) dt for all x in (0, oo) , then

If f(x) = int_(0)^(x) e^(t^(2)) (t-2) (t-3) dt for all x in (0, oo) , then

. If f(x) = int_0^x e^(t^2) (t-2)(t-3) dtfor all x in(0 ,oo), then (a)f has a local maximum at x=2. (b)f is decreasing on (2,3) (c)There exists some c epsilon (0,oo) such that f'(c)=0 (d) f has a local minimum at x=3

if f(x)oversetxunderseto(int)e^(t^2)(t-2)(t-3)dt for all x in(0,oo) , then

If f(x) = ∫et^2(t - 2)(t - 3)dt for t ∈ [0, x] for x ∈ (0, ∞), then (A) f has a local maximum at x = 2 (B) f is decreasing on (2, 3) (C) there exists some c∈(0, ∞) such that f′′(c) = 0 (D) f has a local minimum at x = 3.

Let f(x)={|x|,f or 0<|x|<=2:1, for x=0 Then at x=0,f has (a)a local maximum (b) no local maximum (c)a local minimum (d) no extremum

Let f be a real-valued function defined on interval (0,oo),by f(x)=lnx+int_0^xsqrt(1+sint).dt. Then which of the following statement(s) is (are) true? (A). f"(x) exists for all in (0,oo)." " (B). f'(x) exists for all x in (0,oo) and f' is continuous on (0,oo), but not differentiable on (0,oo)." " (C). there exists alpha>1 such that |f'(x)|<|f(x)| for all x in (alpha,oo)." " (D). there exists beta>1 such that |f(x)|+|f'(x)|<=beta for all x in (0,oo).