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(A) The slope of a graph at any point is given by $	an 	heta$,where $	heta$ is the angle the tangent at that point makes with the positive $x$-axis

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First decreases then increases

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(A) The slope of a graph at any point is given by $	an 	heta$,where $	heta$ is the angle the tangent at that point makes with the positive $x$-axis.$1$. From $A$ to $B$: The tangent makes an acute angle with the $x$-axis. As we move from $A$ to $B$,the angle $	heta$ decreases from a positive value towards $0$ at the peak $B$. Since $	an 	heta$ is positive and decreasing in this interval,the magnitude of the slope decreases.$2$. At point $B$: The tangent is horizontal,so $	heta = 0^\circ$ and the slope is $0$.$3$. From $B$ to $C$: The tangent makes an obtuse angle with the $x$-axis. As we move from $B$ to $C$,the angle $	heta$ increases from $0^\circ$ towards $90^\circ$. The slope $(	an 	heta)$ is negative,but its magnitude $|	an 	heta|$ increases as the angle becomes more obtuse.Therefore,the magnitude of the slope first decreases (from $A$ to $B$) and then increases (from $B$ to $C$).The correct option is $A$.

What is the behavior of the magnitude of the slope of the shown graph?

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