Asked by Mathematics
Consider the following function.
f(x) = e^(x)/ x^(4)
(a) Find the intervals of increase or decrease.
(b) Find the intervals of concavity.
(c) Find the point of inflection. (If an answer does not exist, enter DNE.)
(x, y) =
f(x) = e^(x)/ x^(4)
(a) Find the intervals of increase or decrease.
(b) Find the intervals of concavity.
(c) Find the point of inflection. (If an answer does not exist, enter DNE.)
(x, y) =
Answers
Damon
dy/dx = [x^4 e^x - 4 x^3 e^x]/x^8
= [ x e^x - 4 e^x ] / x^5
= 0 when x = 4
increasing if x>4
decreasing if x <4
what is sign of second derivative?
It is a pain to compute, sketch graph of slope'
http://www.wolframalpha.com/input/?i=plot+[+x+e^x+-+4+e^x+]+%2F+x^5
sure looks like inflection point at x = 4
= [ x e^x - 4 e^x ] / x^5
= 0 when x = 4
increasing if x>4
decreasing if x <4
what is sign of second derivative?
It is a pain to compute, sketch graph of slope'
http://www.wolframalpha.com/input/?i=plot+[+x+e^x+-+4+e^x+]+%2F+x^5
sure looks like inflection point at x = 4