Let a function


Let a function $f:[0,5] \rightarrow \mathbf{R}$ be continuous, $f(1)=3$ and $F$ be defined as :

$F(x)=\int_{1}^{x} t^{2} g(t) d t$, where $g(t)=\int_{1}^{t} f(u) d u$.

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.

Correct Option: 1


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