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Question Number 203063 by LowLevelLump last updated on 09/Jan/24

Answered by MM42 last updated on 09/Jan/24

$$f^{\prime }=e^x-a=0\Rightarrow \alpha =lna$$$$\Rightarrow minf=a-alna$$$$g^{\prime }=a-\frac{1}{x}=0\Rightarrow \beta =\frac{1}{a}$$$$\Rightarrow ming=1+lna$$$$\Rightarrow minf=ming\Rightarrow a-alna=1+lna$$$$\Rightarrow a-1=(a+1)lna\Rightarrow a=1✓$$$$\Rightarrow f=e^x-x\mathrm{\&}g=x-lnx$$$$$$

Commented by MM42 last updated on 09/Jan/24

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