Graph the function f(x)=3e−x23f(x)=$$3e^{-\frac{x^2}$${3}}. f′(x)=−2xe−$$x2/3f^{\prime}(x$$)=$$-2xe^{-x^2/3}f$$′′(x)=e−x2/3(4x23−$$2)f^{\prime\prime}(x$$)=$$e^{-x^2/3}$$\left(\frac{$$4x^2$$}{3}-2\right)

5. Graphical Applications of Derivatives

5. Graphical Applications of Derivatives / Curve Sketching / Problema 10

Problema 10

Graph the function $f (x) = 3 e^{- \frac{x^{2}}{3}}$ .
$f^{'} (x) = - 2 x e^{- x^{2} / 3}$
$f^{''} (x) = e^{- x^{2} / 3} (\frac{4 x^{2}}{3} - 2)$

Graph of the function f(x)=3e^(-x²/3), showing a curve with a minimum at x=0 and approaching y=0 as x moves away from zero.

Graph of the function f(x)=3e^(-x²/3), showing a peak at y=3 and approaching y=0 as x moves away from 0.

$Graph of the function f(x)=3e^{-x^2/3}, showing a blue curve with a maximum at (0, -4) and extending downwards.$

Graph of the function f(x)=3e^(-x²/3), showing a blue curve with a minimum at (0, 3) on a grid.