Calculus
# Extrema

$y=f(x).$ Let $a$ be the $x$-coordinate of the intersection point between the curve and negative part of the $x$-axis, and let $b$ and $c$ be the $x$-coordinates of the local maximum and minimum of the curve, respectively, as shown in the diagram. If $a = -3, b = 4, c = 7,$ and $f'(x)>0$ for the portions of the curve that are not displayed in the diagram, what is the range of $x$ that satisfies $f(x)f'(x) > 0?$

The above diagram shows the curve