Find f(x) if f(1) = -1 and the tangent line at (x, f(x)) has slope 2e^x + 1
This is a problem that was thrown into my indefinite integral homework, and I'm kinda stuck.
any help appreciated.
the derivative gives the slope. thus if the slope at any $\displaystyle x$ is $\displaystyle 2e^x + 1$ it means that:
$\displaystyle f'(x) = 2e^x + 1$
$\displaystyle \Rightarrow f(x) = \int f'(x)~dx$
and use the fact that $\displaystyle f(1) = -1$ to solve for the arbitrary constant of integration