(Solved): Let \( f(x) \) be a differentiable function on \( \mathbb{R} \). The figure below is the graph of t ...

Let \( f(x) \) be a differentiable function on \( \mathbb{R} \). The figure below is the graph of the derivative of \( f(x) \). Which of the following is true for the extrema of the function \( f(x) ? \) A Local maximum at \( x=-2 \). local minimum at \( x=2 \) and \( x=0 \), and there is no other critical point with an extremum, B Local maximum at \( x=1 \), local minimum at \( x=-1 \), and a critical point at \( x=2 \) with no extremum, c. Local maximum at \( x=-3 \), local minimum at \( x=-1 \), and critical points at \( x=-2 x=0, x=2 \) with no extremum. D. Local maximum at \( x=0,10 c a l \) minimum at \( x=-2 \) and a critical point at \( x=2 \). with no extremum, E Local maximum at \( x=-2 \). local minimum at \( x=0 \), and a critical point at \( x=2 \) with no extremum.