1. ## Integral problem

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.

2. Originally Posted by leviathanwave
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 $x$ is $2e^x + 1$ it means that:

$f'(x) = 2e^x + 1$

$\Rightarrow f(x) = \int f'(x)~dx$

and use the fact that $f(1) = -1$ to solve for the arbitrary constant of integration