Hi, I have tried to solve this and I can't. I am on my last try (4/5 only 1 try left!!) and I would really appreciate it if someone could solve this?

Find all critical numbers of,

f(x)=x^(4)*e^(-19x)

Hint:: f(x)=(4x^(3)−19x^(4))e^−(19x)

x=?

Express your answer using set notation. That is, list all solutions separated by commas and enclosed in braces { }.

## Answers (1)

Alright, they provide the derivative, that's helpful.

So 0=(e^-19x)(4x^(3)-19(x^4))

Because e^-19x will always be positive, you can ignore that and focus on setting the other factor equal to 0.

0=4x^3-19x^4

Factor out x^3 --> 0=(x^3)(4-19x)

Now you can set each of these equal to 0

0=x^3 and 0=4-19x

x=0 x=4/19

x={0, 4/19}

Reference:Physics major at Princeton University