Maths · Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable
The point for the curve is
The point for the curve \( y=x e^{x} \) is
- A. \( x=-1 \) is minimum
- B. \( x=0 \) is minimum
- C. \( x=-1 \) is maximum
- D. \( x=0 \) is maximum
Step-by-step solution
Differentiate y = x e^x to get y' = e^x (1+x). Set y'=0 gives x=-1. Second derivative y'' = e^x (x+2). At x=-1, y''=e^{-1}>0, so x=-1 is a point of local minimum.
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