Problem

Find all values of $x$ where the graph of $f(x)=\left(-4 x^{2}+x\right) e^{-4 x}$ has an inflection point.

Solution

Step 1 :Find the second derivative of the function \( f(x) = (-4x^2 + x)e^{-4x} \)

Step 2 :Set the second derivative equal to zero and solve for \( x \)

Step 3 :The inflection points are \( x = \frac{1}{4} \) and \( x = 1 \)

Step 4 :Final Answer: \( \boxed{\frac{1}{4}, 1} \)

From Solvely APP
Source: https://solvelyapp.com/problems/Jd9p06CDMR/

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