Question

What is the value of the slope of the tangent line to a relative maximum of a function?​

Answer 1

Slope is zero at relative maximum.

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
`y = b`, where,
`b` is the y intercept of the line.

Also,
`y = b` can be rewritten in slope-intercept form as:

`y = 0x + b`

On comparing the above equation with the standard form
`y = mx + b`, we conclude that,
`m = 0` for the line
`y = b`. Therefore, the slope of the line of the form
`y = b` is 0. Hence, the slope of the tangent line to the relative maximum is zero.