Topic : Critical points of a function, intervals of increase and decrease, extreme points, maximum a

[night bear]

I want to know how to find any type of this math topic questions and , who can give me formulas of this topic

[lethal aspen]

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[night bear]

On the 6th Question it asks how many extremium points there are have?

[heady bronze]

@night bear Do you know how to figure out if something is an extremium?

[true hound]

Use Fermat's Theorem (Interior Extremum Theorem) and first derivatives

[lethal aspen]

@night bear

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[elder rapids]

generally just calculate the 1st derivative of the function and find where its positive and where its =0. Due to fermat's theorem, if a point is an extremant, then the 1st derivative must be equal to 0 there.
Also, if the 1st derivative switches signs before and after a point (which is not necessarily derivable), you can say that the point is an extremant (criterion for extremant points)

so yea pratically just ask f'(x) major and equal to 0, and look where it switches signs

[true hound]

And with the first derivative on the domain before and after that critical point, make sure both are continuous on the open interval

Only then may you use an arbitrary test point in each interval

[elder rapids]

yup that too

[night bear]

Ohh thanks everyone , i understand

@elder rapids

@true hound

Thanks

[true hound]

Mhm

[elder rapids]

npp