Given that the graph of $f$ passes through the point $(1, 6)$ and that the slope of its tangent line at $(x, f(x))$ is $2x + 1$, find $f(2)$.

Question

As in the title - we assume that the graph of $f$ passes through $(1,6)$ (i.e. $f(1) = 6$) and that the slope of its tangent line at $(x, f(x))$ is $2x + 1$ and we are asked to find $f(2)$.

How does one go about solving for $f(2)$? It would be greatly appreciated if someone could set me off in the right direction :)

Answer 1

1. Find an equation for $f(x)$ by integration

2. Find the value of the constant using $(1,6)$

3. Evaluate $f$ at $x=2$