Integral problem

**leviathanwave** · November 13th 2007, 09:11 AM

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.

**Jhevon** · November 13th 2007, 09:14 AM

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

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