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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 { }.
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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