Pregunta
EVT Find the maximum and minimum values of
on the interval
Ask by Clarke Chan. in Canada
Mar 14,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The minimum value of
on the interval
is
at
, and the maximum value is
at
.
Solución
Let
on the interval
.
Step 1. Find the derivative
We compute
Step 2. Find critical points
Critical points occur when
or when
is undefined. Since
is defined everywhere, we need to solve:
Within the interval
, the solutions of
are:
Step 3. Evaluate the function at the critical points and endpoints
- At
: - At
: - At
: - At
:
Step 4. Compare the values
Let us approximate the numerical values to compare:
-
. -
. -
. -
.
Thus, the smallest value is
and the largest value is
.
Final Answer
The minimum value of
on
is
(at
), and the maximum value is
(at
).
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg


Mind Expander
To find the maximum and minimum values of the function
on the interval
, we must first identify the critical points by taking the derivative and setting it to zero.
-
Find the derivative:
-
Set the derivative to zero and solve for critical points:The solutions for
in the interval are: -
Evaluate
at the critical points and endpoints: -
At
: -
At
: -
At
: -
At
:
-
-
Compare the evaluated values:
-
-
Determine maxima and minima:
- The minimum value occurs at
. - The maximum value occurs at
.
- The minimum value occurs at
Thus, the maximum value of
on the interval
is
, and the minimum value is
.
preguntas relacionadas

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