If f(x) = 2 x t 0 e (t 2)(t 3)dt for all 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

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

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

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

if f(x) = int_(0)^(x) (t^2+2t+2) dt where x in [2,4] then

If F(x) =int_(x^(2))^(x^(3)) log t dt (x gt 0) , then F'(x) equals

Let f(x)={(1+sin(x), if x lt 0), (x^2-x+1, if x >= 0):}, then: (a) f has local maximum at x=0, (b). f has local minimum at x=0, (c) f is increasing everywhere, (d) f is decreasing everywhere.

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

If f(-x)+f(x)=0 then int_(a)^(x)f(t)dt is