Monday

September 15, 2014

September 15, 2014

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

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

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 - 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 - 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 ...

Calculus - What is the point of inflection of the function f(x)=x^3-8x^2+5x+50? ...

Calculus - Graph the following function. Find and state the domain, intercepts, ...

Calculus - 1. For the function f(x)=4x^3-30x^2+4: a) Find the critical numbers ...

high school calculas - Find the (a) the local extrema, (b) the intervals on ...

trig - use the function G(x)=x^3-8x +1 b) identify and verify the y intercept of...