Question

IF F'(x)=0, what does that mean
with respect to the tangent line?​

Answer 1

Step-by-step explanation:

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Answer 2

The tangent line would be parallel to the x-axis and would be horizontal.

Given

• F'(x)=0
• tangent line

To find

• The physical meaning of the mathematic equation provided.

Solution

we are provided with a real valued function (as it is assumed ) f(x) and it's first derivative which is equal to zero and we are asked to explain its physical meaning about the condition provided.

Previous knowledge

we know that the first derivative of a function gives the slope of the function at a point, or equation to estimate the slope of the function.

we also know that the slope of the x-axis would be zero and that of y axis would be infinity.

To the question

Therefore a line with the slope zero would be parallel to the x-axis or in general sense it is simply called a horizontal tangent line.

Hence, in the above condition the tangent line would be parallel to the x-axis and would be horizontal (as it has the same slope of x axis)

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