State the signs of and on the interval (0,2). A) f ' 0 f '' 0 f '' 0 E) f '

Question

State the signs of and on the interval (0,2). A) f ' < 0 f '' = 0 B) f ' < 0 f '' > 0 C) f ' > 0 f '' < 0 D) f ' > 0 f '' > 0 E) f ' < 0 f '' < 0

Quizplus · Accepted Answer

According to the given notation, 11ea8970_6a2c_bace_861b_c110f208fa49_TB1301_11 represents a function f(x) with its derivative f'(x) and second derivative f''(x) being negative on the interval (0,2), while 11ea8970_6a2c_bacf_861b_33da658f03c9_TB1301_11 represents a function g(x) with its derivative g'(x) being negative and second derivative g''(x) being positive on the interval (0,2). Hence, the sign of the first derivative changes from negative to positive at some point in the interval, while the sign of the second derivative remains the same throughout the interval. This behavior is characteristic of a function that has a local maximum at some point in the interval. Therefore, the best choice is B, where f'(x) < 0 and f''(x) > 0 on (0,2).

​State the Signs of and on the Interval

State the Signs of and on the Interval