AP Calculus: Let f(x) = 2xe^2x;find limits,abs. minimum

[venialove]

Let f be the function defined by f(x)= 2xe^2x

A. Find lim x-> -? f(x) and lim x-> ? f(x)

B. Find the absolute minimum value of f.


This is what I did
f(x) = 2x/(e^(-x))
f(x) = 2x*(e^x)

f'(x) = 2xe^x + e^x*2
f'(x) = 2xe^x + 2e^x

f''(x) = 2xe^x + 2e^x + 2e^x
f''(x) = 2xe^x + 4e^x

Solve for the roots of f'':
0 = 2xe^x + 4e^x
-4e^x = 2xe^x
-4 = 2x
-2 = x

 

[skeeter]

Re: ap calculus

Let f be the function defined by f(x)= 2xe^2x

A. Find lim x-> -? f(x) and lim x-> ? f(x)

B. Find the absolute minimum value of f.


This is what I did
f(x) = 2x/(e^(-x)) is f(x) = 2x*e[sup:3tfhk1jn]x[/sup:3tfhk1jn] or 2x*e[sup:3tfhk1jn]2x[/sup:3tfhk1jn] ?
f(x) = 2x*(e^x)

f'(x) = 2xe^x + e^x*2
f'(x) = 2xe^x + 2e^x

f''(x) = 2xe^x + 2e^x + 2e^x
f''(x) = 2xe^x + 4e^x

Solve for the roots of f'':
0 = 2xe^x + 4e^x
-4e^x = 2xe^x
-4 = 2x
-2 = x

 

[venialove]

2x*e2x

 

[stapel]

Let f be the function defined by f(x)= 2xe^2x
A. Find lim x-> -? f(x) and lim x-> ? f(x)
B. Find the absolute minimum value of f.

This is what I did
f(x) = 2x/(e^(-x))
f(x) = 2x*(e^x)

f'(x) = 2xe^x + e^x*2

Since you're differentiating, I'll guess that you're working on Part (B), having completed Part (A) already. But the function you're using is not the one you started with, so at least one of them is incorrect.

Kindly reply with clarification. Thank you!

Eliz.