Consider the function f(x) = 7 xe^{-7.5 x}, 0<_x<_2.

Question

This function has an absolute minimum value equal to:

which is attained at x=

Answer 1

First step is usually to find the derivative:

f = 7xe^(-7.5x)
f' = 7e^(-7.5x) + 7xe^(-7.5x)(-7.5)
= 7e^(-7.5x) (1-7.5x)

since e^(ax) is never zero, we just need to see when (1-7.5x) = 0.

I think you can take it from there.

The graph is at

http://www.wolframalpha.com/input/?i=7xe^%28-7.5x%29+for+-.1+%3C+x+%3C+.5

Be careful. It's almost a trick question.