Question

How do you use the limit definition to find the slope of the tangent line to the graph `f(x) = 2x+4` at (1, 6)?

Answer 1

`2`

Explanation:

We have: `f(x) = 2 x + 4`

`=> f'(x) = lim_(h -> 0) (f(x + h) - f(x)) / (h)`

`=> f'(x) = lim_(h -> 0) (2 (x + h) + 4 - 2 x + 4) / (h)`

`=> f'(x) = lim_(h -> 0) (2x + 2 h - 2 x) / (h)`

`=> f'(x) = lim_(h -> 0) (2h) / (h)`

`=> f'(x) = 2`