Contemporary English Version An effective female’s relatives are held along with her by this lady wisdom, it will likely be shed because of the the woman foolishness.

Douay-Rheims Bible A smart lady buildeth this lady domestic: although foolish tend to down together hands that also that’s established.

Worldwide Simple Adaptation The smart lady accumulates this lady home, nevertheless stupid that tears it down together with her individual hands.

The fresh Changed Important Adaptation The new wise woman generates this lady household, nevertheless the foolish rips they down with her own hands.

The new Center English Bible Most of the smart girl stimulates their domestic, however the dumb one to tears it down with her individual give.

## World English Bible Most of the wise lady builds their family, although dumb you to definitely rips they down with her very own give

Ruth 4:eleven “We’re witnesses,” said the brand new elders and all of the people in the gate. “Can get the father result in the girl entering your property such as Rachel and Leah, which together with her built up the house from Israel. ous within the Bethlehem.

Proverbs A dumb man is the disaster of his father: and the contentions from a partner try a repeating shedding.

Proverbs 21:9,19 It is advisable so you can stay into the a corner of the housetop, than just with good brawling lady into the a wide house…

Definition of a horizontal asymptote: The line y = y_{0} is a “horizontal asymptote” of f(x) if and only if f(x) approaches y_{0} as x approaches + or – .

Definition of a vertical asymptote: The line x = x_{0} is a “vertical asymptote” of f(x) if and only if f(x) approaches + or – as x approaches x_{0} from the left or from the right.

Definition of a slant asymptote: the line y = ax + b is a “slant asymptote” of f(x) if and only if lim _{(x–>+/- )} f(x) = ax + b.

Definition of a concave up curve: f(x) is “concave up” at x_{0} if and only if is increasing at x_{0}

Definition of a concave down curve: f(x) is “concave down” at x_{0} if and only if is decreasing at x_{0}

The second derivative test: If f exists at x_{0} and is positive, then is concave up at x_{0}. If f exists and is negative, then f(x) is concave down at x_{0}. If does not exist or is zero, then the test fails.

Definition of a local maxima: A function f(x) has a local maximum at x_{0} if and only if there exists some interval I containing x_{0} such that f(x_{0}) >= f(x) for all x in I.

## The first derivative take to to have local extrema: If the f(x) is increasing ( > 0) for all x in a few interval (a, x

Definition of a local minima: A function f(x) has a local minimum at x_{0} if and only if there exists some interval I containing x_{0} such that f(x_{0}) <= f(x) for all x in I.

Density regarding regional extrema: All local extrema can be found at the crucial things, but not all vital things exists within local extrema.

_{0}] and f(x) is decreasing ( < 0) for all x in some interval [x_{0}, b), then f(x) has a local maximum at x_{0}. If f(x) is decreasing ( < 0) for all x in some interval (a, x_{0}] and f(x) is increasing ( > 0) for all x in some interval [x_{0}, b), then f(x) has a local minimum at x_{0}.

The second derivative test for local extrema: If = 0 and > 0, then f(x) has a local minimum at x_{0}. If = 0 and < 0, then f(x) has a local maximum at x_{0}.

Definition of absolute maxima: y_{0} is the “absolute maximum” of f(x) on I if and only if y_{0} >= f(x) for all x on I.

Definition of absolute minima: y_{0} is the “absolute minimum” of f(x) on I if and only if y_{0} <= f(x) for all x on I.

The ultimate well worth theorem: In the event the f(x) was carried on for the a close period I, then f(x) has actually a minumum of one absolute restrict plus one absolute lowest inside I.

Occurrence out of pure maxima: In the event that f(x) is proceeded inside a close period We, then your pure restriction away from f(x) within the We ‘s the limit value of f(x) to the the regional maxima and you will endpoints to your I.

Thickness regarding pure minima: When the f(x) is actually continuous during the a close period I, then absolute at least f(x) within the I ‘s the lowest property value f(x) to the most of the regional minima and you can endpoints towards the I.

Solution variety of interested in extrema: In the event that f(x) is actually proceeded for the a close period We, then pure extrema from f(x) in the We occur at the vital issues and you will/or on endpoints from I. (This might be a less particular style of the above mentioned.)