Question

If f(x) = xe^−x, find the value of x at which the graph of y = f(x) has a horizontal tangent
line.

Answer 1

You need to find the derivative and set it equal to zero. Remember that a horizontal tangent always has slope zero. Do you know how to find this derivative?

Answer 2

i think so... would it be -e^-x ?

Answer 3

No. Can you use the product rule?
\[\frac{ d }{ dx }(ab)=a'b+ab'\]

Answer 4

e^x + x(-e^-x) ??
if that's not right then i have no idea how to take the derivative of e^-x

Answer 5

It's right except that you dropped a negative sign in "e^x", which should be e^-x

Answer 6

oh yea, that's what i meant.

Answer 7

so now what?

Answer 8

I suggest that you factor out e^-x since no finite x can make that equal to 0:
e^-x(1-x)

Answer 9

Do you see what I mean?

Answer 10

yep, i get that much.

Answer 11

Sorry about that....So you think you can solve the problem, knowing the derivative and the slope of all horizontal tangents (=0)?

Answer 12

yeahh, it's 1 right?

Answer 13

Yes!

Answer 14

Thx for recognition

Answer 15

thanks for the help :)