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.

The function f(x)= x/2 + 2/x ​ has a local minimum at

The function f(x) = (x)/( 2) + (2)/( x) has a local minimum at

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

The function f(x)=x/2+2/x has a local minimum at (a) x=2 (b) x=-2 (c) x=0 (d) x=1

Let f(x) = int_(0)^(x)|2t-3|dt , then f is

If f(x)=int_0^x(sint)/t dt ,x >0, then (a) f(x) has a local maxima at x=npi(n=2k ,k in I^+) (b) f(x) has a local minima at x=npi(n=2k ,k in I^+) (c) f(x) has neither maxima nor minima at x=npi(n in I^+) (d) (f)x has local maxima at x=npi(n=2k -1, k in I^+)

The function f(x)=2x^(3)-3(a+b)x^(2)+6abx has a local maximum at x=a , if

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

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

A function f is defined by f(x)=int_0^pi costcos(x-t)dt, 0lexle2pi . Which of the following hold(s) good? (A) f(x) is continuous but not differentiable in (0,2pi) (B) There exists at least one c in (0,2pi) such that f\'(c)=0 (C) Maximum value of f is pi/2 (D) Minimum value of f is -pi/2