Question

How do you find the slope of the tangent line to the graph of the function `f(x)=x^2-4` at (1,-3)?

Answer 1

See explanation.

Explanation:

The slope of a tangent line at `(x_0,f(x_0))` is equal to the value of the first derivative at `x_0`: `f^'(x_0)`.

Here we have:

`f(x)=x^2-4`

`f^'(x)=2x`

`f^'(1)=2`

Answer The slope of the tangent line at `x_0=1` is `2`.