calculus function question

Question

The factored forms of f'(x) and f''(x) are shown below.

f '(x) = e^(−x)[ (x − 3)^2 (x − 5)]

f ''(x) = = −e ^(−x) [ (x − 7)(x − 3)(x − 4)]

interval(s) where f(x) is increasing: ??

interval(s) where f(x) is decreasing: ??

local minimum(s): local maximum(s): ??

interval(s) where f(x) is concave up: ??

interval(s) where f(x) is concave down: ??

inflection point(s): ??

the e in both derivatives is confusing to me. For increasing/decreasing I found that f(x) using the first derivative, increases on the interval 5 < x , and decreases on x < 3, and increases on 3 < x < 5 (not sure about this one) and I don't know what to do with the e. the rest I am very unsure how to do.

Answer 1