`f(x)=int_0^(x^2)(t^2-5t+4)/(2+e^t)dt` Find the number of points of local maximum and local minima

For x in (0,(5pi)/2) , define f(x)""=int_0^xsqrt(t)sint"dt" Then f has : local maximum at pi and 2pi . local minimum at pi and 2pi local minimum at pi and local maximum at 2pi . local maximum at pi and local minimum at 2pi .

Find the points of local maxima,local minima and the points of inflection of the function f(x)=x^(5)-5x^(4)+5x^(3)-1. Also,find the corresponding local maximum and local minimum values.

Find the points of local maxima,local minima and the points of inflection of the function f(x)=x^(5)-5x^(4)+5x^(3)-1. Also,find the corresponding local maximum and local minimum values

Let f(x) = int_(0)^(x)(t-1)(t-2)^(2) dt , then find a point of minimum.

f(x) = int_(x)^(x^(2))(e^(t))/(t)dt , then f'(t) is equal to :

f(x)={c^x ,0lt=x1 2-c^(x-1),1

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) 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