ਕੋਈ ਵੀ ਗਣਿਤ ਸਮੱਸਿਆ ਹੱਲ ਕਰੋ

ਕਦਮ ਦਰ ਕਦਮ

1. f(x) = x e^{- x}

   Critical points are where f′(x) = 0 or is undefined.

2. f'(x) = - x e^{- x} + e^{- x}

   Differentiate.

3. x = 1

   Solve f′(x) = 0.

4. f''(x) = x e^{- x} - 2 e^{- x}

   Second-derivative test: f″ < 0 → maximum, f″ > 0 → minimum.

5. f''(1) = - \frac{1}{e} \Rightarrow (1, e^{-1}) \text{ is a local maximum}