Question

Question in attachment answer with work no spam

Answer 1

The derivative of a function at a point gives the slope of the line tangent to the function's graph at that point.

Therefore,
`f'(2)` gives the slope of the tangent line to the graph of
`f` where
`x=2` , which is the point
`(2,3)`.

We know this line passes through
`(2,3)` , and we are also given that it passes through
`(7,6)`. This should be enough to find the slope of that line.


`\text{Slope} = \frac{\text{change in y}}{\text{change in x}}`


`(6-3)/(7-2)`


`= (3)/(5)`

In conclusion,
`f'(2)=(3)/(5)`