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Undefined.

Proof, let a function f have a vertical line on x = c.

(Notice: By definition of functions, it is not even a function, which means that we do not even need to discuss differentiability. We assume it is a function)

Now suppose f'(c) exist, then

f'(c) = lim x --> c (f(x) - f(c))/(x - c), the limit exist but since it's a straight line, assume non trivial (a point), we have automatically x = c. But since it's non-trivial, hence f(x) != f(c), let f(x) - f(c) = r for some real number r != 0.

we get f'(c) = lim x --> c (f(x) - f(c)) / (x - c) = r/0 which is undefined.

Contradiction!.

Hence f'(c) doesn't exist.

Note: If you see a straight line some where on a "function" and they ask for derivative, write:"This is not a function, what kind of question is this! Go back to Calculus class!"

If you are discussing a function with a vertical slope, e.g. let f(x) = cubeRoot(x), then it's a different proof.

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Q: What are the slopes of vertical lines?
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Related questions

What has to be true about the slopes of two perpendicluar lines that's neither vertical?

The slopes are negative reciprocals.


When is the product of the slopes of two perpendicular lines not equal to -1?

When the perpendicular lines are horizontal and vertical.


If two lines are parallel what do you know about their slopes?

If two lines are parallel, they have the same slope.(And if they are perpendicular, the product of their slopes is minus one - unless one line is horizontal and the other vertical.)


What must be true about the slopes of two perpendicular lines neither of which is vertical?

In that case, the product of the slopes is equal to minus 1.


How many slopes do vertical lines have?

The slope of a vertical line is undefined. The slope of a horizontal line is 0. Hope this helps.


What is true about the slope of parallel lines?

The slopes will be the same. It is also possible that both parallel lines have no slope defined - if they are vertical.


How do slopes of perpendicular lines compare?

Slopes of perpendicular lines will be opposite reciprocals. This means that the slopes have opposite signs and that one is 1/ the other. For example, 2 and -1/2.


What is the definition of a slope of parallel lines?

Horizontal lines have a slope of zero, and the slope of vertical lines is undefined. Parallel lines have equal slopes, and perpendicular lines have slopes that are negative reciprocals of each other. So we can say that: Two nonvertical lines are parallel if and only if they have the same slope. Two lines are perpendicular if and only if their slopes are negative reciprocals of each other. That is, if the slopes are m1 and m2, then: m1 = - 1/m2 or (m1)(m2) = -1


What can you say about the slopes of two non-vertical perpendicular lines?

They are negative reciprocals Ex -1/2 and 2


If two lines are their slopes are negative reciprocals?

If the lines are perpendicular, their slopes are negative reciprocals.If the lines are perpendicular, their slopes are negative reciprocals.If the lines are perpendicular, their slopes are negative reciprocals.If the lines are perpendicular, their slopes are negative reciprocals.


What is the difference between slopes of parallel lines and slopes of perpendicular lines?

Slopes of parallel lines have the same slope (they are changing at the same rate).Slopes of perpendicular lines have slopes that are the negative inverse of each other, that is, their product is -1. (The slope of a vertical line is therefore undetermined, not infinity. There is no slope s that times 0 equals -1.)---Let m1 be the slope of line one and m2 be the slope of line two. Then:If the lines are parallel, then their slopes are equal, so m1 - m2 = 0.If the lines are perpendicular, then their slopes are negative inverses of each other, so= m1 - (-1/m1)= m1 + 1/m1= (m12 + 1)/m1


If two lines have slopes that are negative reciprocals of each other then they are if they have slopes that are the same then they are?

negative reciprocal slopes ---> the lines are perpendicular equal slopes ---> the lines are parallel