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Show that f(x)=(x-1)e^x+1 is an increasi...

Show that `f(x)=(x-1)e^x+1` is an increasing function for all `x > 0.`

Text Solution

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`f(x)=(x-1) e^{x}+1 `
` f^{prime}(x)=(x-1) e^{x}+e^{x} `
` =x e^{x}-e^{x}+e^{x} `
` =x e^{x} `
Given :` x>0 `
We know
`e^{x}>0 `
` Rightarrow x e^{x}>0 `
` ...
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