Let two real numbers $a$ and $b$ with $a < b$. Consider a function $f$ defined, continuous, strictly increasing on the interval $[a; b]$ and which vanishes at a real number $\alpha$. Among the following propositions, the function in Python language that allows giving an approximate value of $\alpha$ to 0.001 is: a. \begin{verbatim} def racine(a, b): while abs(b - a) >= 0.001: m = (a + b) / 2 if f(m) < 0: b = m else: a = m return m \end{verbatim} c. \begin{verbatim} def racine(a, b): m = (a + b) / 2 while abs(b - a) <= 0.001: if f(m) < 0: a = m else: b = m return m \end{verbatim} b. \begin{verbatim} def racine(a, b): m = (a + b) / 2 while abs(b - a) >= 0.001: if f(m) < 0: a = m else: b = m return m \end{verbatim} d. \begin{verbatim} def racine(a, b): while abs(b - a) >= 0.001: m = (a + b) / 2 if f(m) < 0: a = m else: b = m return m \end{verbatim}
Let two real numbers $a$ and $b$ with $a < b$.\\
Consider a function $f$ defined, continuous, strictly increasing on the interval $[a; b]$ and which vanishes at a real number $\alpha$.\\
Among the following propositions, the function in Python language that allows giving an approximate value of $\alpha$ to 0.001 is:
a.
\begin{verbatim}
def racine(a, b):
while abs(b - a) >= 0.001:
m = (a + b) / 2
if f(m) < 0:
b = m
else:
a = m
return m
\end{verbatim}
c.
\begin{verbatim}
def racine(a, b):
m = (a + b) / 2
while abs(b - a) <= 0.001:
if f(m) < 0:
a = m
else:
b = m
return m
\end{verbatim}
b.
\begin{verbatim}
def racine(a, b):
m = (a + b) / 2
while abs(b - a) >= 0.001:
if f(m) < 0:
a = m
else:
b = m
return m
\end{verbatim}
d.
\begin{verbatim}
def racine(a, b):
while abs(b - a) >= 0.001:
m = (a + b) / 2
if f(m) < 0:
a = m
else:
b = m
return m
\end{verbatim}