Answer:
Slope is zero at relative maximum.
Step-by-step explanation:
If a function has a relative maximum at x =a, then the tangent line to the function at that point is parallel to the x axis.
We know that, a line parallel to x axis is of the form [tex]y = b[/tex], where, [tex]b[/tex] is the y intercept of the line.
Also, [tex]y = b[/tex] can be rewritten in slope-intercept form as:
[tex]y = 0x + b[/tex]
On comparing the above equation with the standard form [tex]y = mx + b[/tex], we conclude that, [tex]m = 0[/tex] for the line [tex]y = b[/tex]. Therefore, the slope of the line of the form [tex]y = b[/tex] is 0. Hence, the slope of the tangent line to the relative maximum is zero.
