Posted by **Abigail ** on Tuesday, June 15, 2010 at 10:30am.

Identify the coordinates of any local extrema of the function y=e^x - e^(2x).

- Calculus -
**MathMate**, Tuesday, June 15, 2010 at 7:04pm
Let

f(x)=e^{x} - e^{2x}

the domain of f(x) is (-∞,∞).

Thus the extrema of f(x) can be found at point(s) where f'(x)=0.

f'(x)=e^{x} - 2e^{2x}

and f'(x)=0 when

e^{x} = 2e^{2x}

2e^{x}=1

x=ln(1/2) (only root)

Since f"(x)=e^{x} - 4e^{2x}

and

f"(-ln(1/2)) = -1/2

we conclude that a maximum exists at x=ln(1/2) since f" is negative.

Can you take it from here?

## Answer This Question

## Related Questions

- math calculus - Find the intervals on which the function f(x)=x²/³(10-x) is ...
- Math - For the function y=(x^4)-(2x^2)+1 Identify all relative extrema. Identify...
- Math - For the function y = x^4-2x^2+1 Identify all relative extrema. Identify ...
- Calculus AB - Find the x-coordinates of any relative extrema and inflection ...
- Pre-Calc/Trig - Identify the extrema for the function. Classify it as a relative...
- Calulus - Consider the function y = 2x^3-3x^2+9x+5. 1. Find where the function ...
- Calculus - Find the local extrema of the function f(x) = (e^x^2+1)/(2x+1) ...
- math - Given the function f(x)=x^4−6x^2 a.) Find all values of x where ...
- Calculus - Find the relative extrema and absolute extrema if any. Use the first ...
- Math - How many x-intercepts and how many local extrema does the polynomial P(x...

More Related Questions