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\noindent {\bf Problem statement} 
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\rightline{Graph of $f'(x)$, the {\it derivative}\/ of $f(x)$}

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\noindent The graph of $y=f'(x)$, the {\it derivative}\/ of the
function $f(x)$, is shown to the right.  (Both parts of this problem,
otherwise unrelated, use information from the graph of the derivative
of $f(x)$.)

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\noindent a) Use information from the graph of $f'(x)$ to find (as
well as possible) the $x$ where the {\it maximum value}\/ of $f(x)$ in
the interval $1\le x\le 3$ must occur. Explain using calculus why your
answer is correct (that is, why the value of $f(x)$ for the $x$ you
select is larger than $f(x)$ at {\it any}\/ other number in the
interval).

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\noindent b) Suppose that $f(3)=5$. Use information from the graph and
the tangent line approximation for}  


\noindent $f(x)$ to find an approximate value of $f(3.04)$. Explain
using calculus and information from the graph why your approximate
value for $f(3.04)$ is greater than or less than the exact value of
$f(3.04)$.













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