Answer
$f(4)=3$ and $f'(4)=\frac{1}{4}$
Work Step by Step
The tangent line $(l):y=f(x)$ is at point $A(4,3)$, so point $A(4,3)$ also lies in $(l)$.
Therefore, $f(4)=3$
The equation of the tangent line $l$ would have the following form: $$(l): y=ax+b$$
Since $l$ passes through point $A(4,3)$, we apply the equation of $l$ to $A$, which means $$4a+b=3\hspace{1cm}(1)$$
$l$ also passes through point $B(0,2)$, we also can apply the equation of $l$ to $B$, which means $$0a+b=2$$$$b=2\hspace{1cm}(2)$$
Apply (2) to (1), we have $$4a+2=3$$$$a=\frac{1}{4}$$
Since $a$ is the slope of the tangent line $l$ at point $A(4,3)$, $f'(4)=a=\frac{1}{4}$
