Question

How do you use the limit definition to find the slope of the tangent line to the graph `f(x) = 7` at (-4,7)?

Answer 1

The slope of the tangent is `0` everywhere.

Explanation:

Whilst the answer could be derived using the definition of the derivative from first principles, and other members are welcome to show this I would suggest first we use common sense.

The graph of `y=f(x)` represents a horizontal line, therefore the tangent to `y=f(x)` is also horizontal everywhere, and therefore the gradient of the tangent is `0` everywhere.