1. ## Finding the intervals

Find the intervals where it is increasing, decreasing, concave up, and concave down, local extreme values, and inflection points.

y=e^x-1-x

I took the derivative and got, e^(x-1) -1+e^(x-1)-x

what to do next?

2. ## intervals

Just to clarify, is the function you have given $y = e^{(x-1)} - x$ ?

3. Originally Posted by nzmathman
Just to clarify, is the function you have given $y = e^{(x-1)} - x$ ?
Yes!

4. If $y = e^{(x-1)} - x$,

Then $\frac{dy}{dx} = \frac{d}{dx} (x-1) * e^{(x-1)} - 1$

and $\frac{d}{dx} (x-1) = 1$

So $\frac{dy}{dx} = e^{(x-1)} - 1$

To solve for local extreme values (maxima and minima), solve $\frac{dy}{dx} = 0$

To solve for where the function is increasing, solve $\frac{dy}{dx} > 0$

To solve for where the function is decreasing, solve $\frac{dy}{dx} < 0$

For concave up and concave down the second derivative is needed.

$\frac{d^2 y}{dx^2} = \frac{d}{dx} . \frac{dy}{dx}$

$\frac{d^2 y}{dx^2} = e^{(x-1)}$

To find where the function is concave up, solve $\frac{d^2 y}{dx^2} > 0$

To find where the function is concave down, solve $\frac{d^2 y}{dx^2} < 0$

To find where the inflection points, solve $\frac{d^2 y}{dx^2} = 0$