Find the maximum value of $x ^ { 4 } e ^ { - 19 x }$ . Restrict your attention to the horizontal span of 0 to
A) 2.11
B) 0.36
C) 4.05
D) 3.78

Question

Quizplus · Accepted Answer

To find the maximum value of the function $f(x) = x^4e^{-19x}$, we can use calculus. Taking the derivative of $f(x)$ with respect to $x$ and setting it to zero will give us the critical points. The derivative is $f'(x) = 4x^3e^{-19x} - 19x^4e^{-19x}$. Setting $f'(x) = 0$ and solving for $x$ gives $x = \frac{4}{19}$, which is approximately 0.21. Evaluating $f(x)$ at $x = \frac{4}{19}$ will give us the maximum value since the second derivative test confirms it's a maximum. The exact maximum value isn't provided in the options, but the process of finding it involves calculus and the critical point calculation.

Find the Maximum Value Of x4e−19xx ^ { 4 } e ^ { - 19 x }x4e−19x

Find the Maximum Value Of $x ^ { 4 } e ^ { - 19 x }$