Question

Given that `y=15x-9` is the line tangent to the function `f(x)` at `x=2`, what is `f(2)` and `f'(2)`?

Answer 1

`f(2) = 21` and `f'(2) = 15`

Explanation:

The graph of `f` intersects the tangent line at `x = 2` and the point on the line at `x=2` has `y = 15(2)-9=21`

`f'(2)` is the slope of the line tangent to the graph at `x=2`, and the graph of the given line is `15`, so `f'(2) = 15`