Find the relative extremum of by applying the First Derivative Test.
A)relative minimum:
B)relative maximum:
C)relative minimum:
D)relative minimum:
E)relative maximum:

Question

Find the relative extremum of  by applying the First Derivative Test. ​
A)relative minimum: 
B)relative maximum: 
C)relative minimum: 
D)relative minimum: 
E)relative maximum:

Quizplus · Accepted Answer

To apply the First Derivative Test, we need to take the derivative of the given function:
f(x) = 11eac44f_ed50_afec_bedf_abf673706039_TB7497_11
f'(x) = 11eac44f_ed50_afec_bedf_abf673706039_TB7497_11'

f'(x) = 44eac44f_1111_1111_8113_bedf_da2b1edc79d8_TB7497_11eac44f_ed50_afec_bedf_abf673706039_TB7497_11

To find the critical points, we need to solve the equation:
f'(x) = 0

44eac44f_1111_1111_8113_bedf_da2b1edc79d8_TB7497_11eac44f_ed50_afec_bedf_abf673706039_TB7497_11 = 0

This equation has no real solutions. Therefore, there are no critical points.

Since there are no critical points, we cannot apply the First Derivative Test. However, we can see that the value of the given function is always positive (because 11eac44f_ed50_afec_bedf_abf673706039_TB7497_11 is always positive), so the function has no relative minimum. The only possible relative extremum is a relative maximum, which occurs at every point. Therefore, the best choice is option E.

Find the Relative Extremum of by Applying the First