Find the relative extrema, if any, of $f ( t ) = e ^ { t } - 7 t - 3$. Use the Second Derivative Test, if possible.
A) relative minimum: none, relative maximum: $f ( \ln 3 ) = - 7 \ln 7$
B) relative minimum: $f ( \ln 7 ) = 4 - 7 \ln 7$, relative maximum: none
C) relative minimum: $f ( \ln 3 ) = - 7 \ln 7$, relative maximum: none
D) relative minimum: none, relative maximum: $f ( \ln 7 ) = 4 - 7 \ln 7$

Question

Quizplus · Accepted Answer

The first derivative $f'(t) = e^t - 7$ is zero at $t = \ln 7$. The second derivative $f''(t) = e^t$ is positive at $t = \ln 7$, indicating a relative minimum at $t = \ln 7$.

Find the Relative Extrema, If Any, Of f(t)=et−7t−3f ( t ) = e ^ { t } - 7 t - 3f(t)=et−7t−3

Find the Relative Extrema, If Any, Of $f ( t ) = e ^ { t } - 7 t - 3$