Question

Let a function f:[0, 5] →R be continuous, f(1) = 3 and F be defined as: F(x) = ∫t²g(t)dt for t∈[1, x], where g(t) = ∫f(u)du for u ∈ [1, t].

Then for the function F, the point x = 1 is:

(1) a point of local minima.

(2) not a critical point

(3) a point of inflection.

(4) a point of local maxima.

Answer 1

Answer is (2) a point of local minima

Answer 2

Answer is (1) a point of local minima.