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

Question

Accepted Answer

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} )

Answer

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} )

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

Answer

Popular Problems

Find all values of x where the graph of f(x)=(−4x2+x)e−4x has an inflection point.

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Popular Problems

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