Question

If the tangent line of `f(x)` at (6,3) passes through the point (0,2), what is `f'(6)`?

Answer 1

`f'(6) = 1/6`

Explanation:

The gradient of the tangent line at `x=6` has the same value of `f'(6)`.

To calculate the gradient of the tangent line, since it is just a straight line passing through 2 points, you should calculate `frac{Deltay}{Deltax}`.

`frac{Deltay}{Deltax} = frac{3-2}{6-0}`
`=1/6`

Therefore, `f'(6) = 1/6`.