Pregunta
CVU4 - Some Review Problems: Applications of the Derivative
- Explain why
does not have a guraranteed extreme value on the interval
.
Ask by Martin Fowler. in Canada
Mar 29,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The function
does not have a guaranteed extreme value on the interval
because it is undefined at
, which is within the interval.
Solución
- The function is given by
Notice that the denominator factors as
Thus, the function is undefined when
-
The interval under consideration is
. Although is not in this interval, is. Since makes the denominator zero, the function is discontinuous at that point. -
The Extreme Value Theorem guarantees that a continuous function on a closed interval has both a maximum and minimum value. However, since
is not defined (and hence not continuous) at , which is within the interval , the conditions of the theorem are not met. -
Therefore, the function
does not have a guaranteed extreme value on the interval because it is not continuous on the entire interval.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg


Bonus Knowledge
The function
does not have a guaranteed extreme value on the interval
because it is not continuous across the entire interval. Specifically,
has vertical asymptotes where the denominator equals zero, which occurs at
. Since
falls within the interval of interest, the function becomes undefined there, meaning that
can’t be evaluated at that point, violating the conditions needed for the existence of extreme values.
To determine extrema, a function must be continuous on a closed interval, and since
cannot be evaluated at
, we cannot guarantee the presence of extreme values over
. It’s crucial to check for such points of discontinuity before finding the maxima or minima!

¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium