An equation for the line tangent to the graph of the differentiable function $f$ at $x=3$ is $y=4x+6$ . Which of the following statements must be true?
I. $f(0)=6$
II. $f(3)=18$
III. $f'(3)=4$
A. None
B. I and II only.
C. II and III only
D. I, II and III.
My answer is B because the value of the function at $x=3$ must be 18. III is not true since when 3 is plugged into the derivative of the function, the value must be 18. So all the choices with statement III must be incorrect. I am not sure if it's possible to to solve for $f(0)$. I just concluded that B is the correct answer because III must be false.
Slope of the line $y=4x+5$ is $4$. So $f'(3)=4$ is also correct. I) is false and II) and III) are both correct.
If $f(x)=4x+6$ and $g(x)=4x+6+(x-3)^{2}$ then the tanagent line to the graphs of these functions is the same, namely $y=4x+6$. But $f(0)=6$ and $g(0)=15$. This shows that I) is not true.