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If a continuous $f$ defined on the real line $R$, assume positive and negative values in $R$, then the equation $f(x)=0$ has a root in $R$. For example, if it is known that a continuous function $f$ on $R$ is positive at some point and its minimum values is negative, then the equation $f(x)=0$ has a root in $R$.
Consider $f(x)=k e^x-x$ for all real $x$, where $k$ is real constant.Question:
The line $y=x$ meets $y=k e^x$ for $k \leq 0$ at
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If a continuous $f$ defined on the real line $R$, assume positive and negative values in $R$, then the equation $f(x)=0$ has a root in $R$. For example, if it is known that a continuous function $f$ on $R$ is positive at some point and its minimum values is negative, then the equation $f(x)=0$ has a root in $R$.
Consider $f(x)=k e^x-x$ for all real $x$, where $k$ is real constant.Question:
The line $y=x$ meets $y=k e^x$ for $k \leq 0$ at
Solution:
2303 Upvotes
Verified Answer
The correct answer is:
one point
one point
$$
\text { Let } y=x \text { intersect the curve } y=k e^x \text { at exactly one point when } k \leq 0 \text {. }
$$
\text { Let } y=x \text { intersect the curve } y=k e^x \text { at exactly one point when } k \leq 0 \text {. }
$$
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