locate-the-critical-points-of-fx-x3e-2x-and-use-the-second-derivative-test-to-id

Question

Consider the function $f (x) = x^{3} e^{- 2 x}$ . Its critical points are located at $open paren 0 comma 0 close paren$ and $open paren three halves comma 27 over 8 e cubed close paren$ . Use the Second Derivative Test to identify whether these points are local maxima, minima, or neither.

Accepted Answer

Neither maximum nor minimum at $f (x) = x^{3} e^{- 2 x}$ ,

Local maximum at $open paren three halves comma 27 over 8 e cubed close paren$ .

Answer

Local minimum at $f (x) = x^{3} e^{- 2 x}$ ,

Local maximum at $open paren three halves comma 27 over 8 e cubed close paren$ .

Answer

Local maximum at $f (x) = x^{3} e^{- 2 x}$ ,

Local minimum at $open paren three halves comma 27 over 8 e cubed close paren$ .

Answer

Neither maximum nor minimum at $f (x) = x^{3} e^{- 2 x}$ ,

Local minimum at $open paren three halves comma 27 over 8 e cubed close paren$ .

Consider the function f(x)=x3e−2xf\left(x\right)=x^3e^{-2x}. Its critical points are located at (0,0)\left(0,0\right) and (32,278e3)\left(\frac32,\frac{27}{8e^3}\right). Use the Second Derivative Test to identify whether these points are local maxima, minima, or neither.

Consider the function $f (x) = x^{3} e^{- 2 x}$ . Its critical points are located at $open paren 0 comma 0 close paren$ and $open paren three halves comma 27 over 8 e cubed close paren$ . Use the Second Derivative Test to identify whether these points are local maxima, minima, or neither.