The is the statement of the Mean Value Theorem from your $te\times tb00k$
$Tneoren$ $m4.5$ $Ne8n$ Value Theorem
Let f be continuous over $leclose$ interval $\left(a.b\right)aod$ $i$ $eo$ $xd$ $csnlc$ $\left(ab\right)$ $mmd$
exists at least one point cE $\left(a.b\right)$ $si1dhtba$
$f^{'}\left(c\right)=\dfrac {f\left(b\right)-f\left(a\right)} {b-a}$
What is the geometric interpretation of the conclusion of the theorem?
O The tangent line to the graph of \(f\left(x\right)\) at $l\left(c1\right)$ is parallel to the
secant line connecting \(\left(a,f\left(a\right)\right)\) and
\(\left(b,f\left(b\right)\right)\).
O The tangent line to the graph of $\left(f\left(lef\left(x\left(right\right)$ at \(c\) is the secant line
connecting \(\left(a,f\left(a\right)\right)\) $ana$ \(\left(b,f\left(b\right)\right)\).
O The tangent line to the graph $of$ $\left(f\left(leF\left(x\left(right\right)\left(\right)at1\left(c1\right)is$ perpendicular to the
secant line connecting \(\left(a,f\left(a\right)\right)\) and
A(\left(b,f\left(b\right)\right)\).
O The tangent line to the graph of $\left(fleH\left(x\right)nght\right)\right)\right)$ $at$ $\left(c\right)\right)ishoizonta|$
$Tnere$ is more than one tangent line to the graph $0no$ $\left(flcf\left(x\right)night\right)\left($ $at1\left(c1\right)$