Question

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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. 

$\text{Slope} = \dfrac{\text{change in y}}{\text{change in x}}$ 

$\dfrac{6-3}{7-2}$ 

$= \dfrac{3}{5}$ 

In conclusion, $f'(2)=\dfrac{3}{5}$