Question
Given that $f$ and $g$ are continuous on $[a, b]$ such that $f(a)>g(a)$ and $f(b)<g(b),$ show that there is a number $c$ in $(a, b)$ such that $f(c)=g(c) .$ [Hint: Consider the function $f-g .]$
Step 1
Since $f$ and $g$ are continuous on $[a, b]$, $h$ is also continuous on $[a, b]$. Show more…
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