The derivative of a function at a point gives the slope of the line tangent to the function's graph at that point.
Therefore, [tex]f'(2)[/tex] gives the slope of the tangent line to the graph of [tex]f[/tex] where [tex]x=2[/tex] , which is the point [tex](2,3)[/tex].
We know this line passes through [tex](2,3)[/tex] , and we are also given that it passes through [tex](7,6)[/tex]. This should be enough to find the slope of that line.
[tex]\text{Slope} = \dfrac{\text{change in y}}{\text{change in x}} [/tex]
[tex] \dfrac{6-3}{7-2} [/tex]
[tex]= \dfrac{3}{5} [/tex]
In conclusion, [tex]f'(2)=\dfrac{3}{5}[/tex]
