. 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

Let f(x)=int_(0)^(x)e^(t)(t-1)(t-2)dt. Then, f decreases in the interval

If f(x)=int_(0)^(x)e^(-t)f(x-t)dt then the value of f(3) is

The function f(x)=int_(-1)^(x)t(e^(t)-1)(t-1)(t-2)^(3)(t-3)^(5)dt has a local minimum at x=0(b)1(c)2(d)3

Write True/False: If f'( c ) exists and f'( c )gt0 , then f(x) has a local minimum at x=c.

if f(x)=int_(-1)^(x)t(e^(t)-1)(t-1)(t-2)^(3)(t-3)^(5)dt has a local minimum then sum of values of x