The Second Derivative Test asserts that
- f'(c) = 0 and f''(c) > 0 implies that f has a local minimum at c
- f'(c) = 0 and f''(c) < 0 implies that f has a local maximum at c.
Intuitively, f''(c) > 0 means a smiley face so any critical number of f where f'(c) = 0 should result in a local minimum, the local bottom extreme of the happy face. f''(c) < 0 means a frowning face so any critical number of f where f'(c) = 0 should result in a local maximum, the local top extreme of the happy face
It is inconclusive when f''(c) = 0 or f''(c) does not exist. (For example, consider
. It has no local maxima or minima, yet
and
.)
Therefore,
- From f’(3) = 0 and f’’(3) = -2, we can conclude that f has a local maximum at 3.
- From f’(-2) = 0 and f’’(-2) = 2, we can conclude that f has a local minimum at -2.
- From f'(4) = 0 and f''(4) = 0, we cannot conclude anything from just those two pieces alone. We cannot determine if f has a local maximum or minimum at 4, nor can we say anything about inflection points since we do not know if f'' changes sign at x = 4.
The question is incomplete. The complete question is :
A survey was done to determine the relationship between gender and subject preference. A total of 56 students were surveyed to determine if they liked math, English, social studies, or science as their favorite subject. The results were then broken down based on whether the respondent was male or female.
Which of the following is the closest to the joint relative frequency of being a male who likes social studies ?
Solution :
A two way table used in statistics and mathematics is used to show the frequencies or the relative frequencies for any two categorical variables. One of the category is represented by the rows while the other categories by a column.
Here, in this table it is given that the total surveyed = 56 students
From the table, we know that number of males who likes social studies = 8
Therefore, the closest to the joint relative frequency for being a male who likes the subject social studies is given by :
![$=\frac{8}{56}$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B8%7D%7B56%7D%24)
![$=\frac{1}{7}$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B1%7D%7B7%7D%24)
=0.14
3(x - 2) = 12
Distribute 3 inside the parentheses.
3x - 6 = 12
Add 6 to both sides.
3x = 18
Divide both sides by 3.
![\boxed {x =6}](https://tex.z-dn.net/?f=%20%5Cboxed%20%7Bx%20%3D6%7D%20)
Answer:
b
Step-by-step explanation:
you see is equal it means that on might likely to be a boy