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- idku

just reviewing something from calc 1
(made up ex.)

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- idku

just reviewing something from calc 1
(made up ex.)

- schrodinger

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- idku

Should I make a function up?
\(\tt f(x)=x^3+3x^2+2x+1\)
now will do a lot of things to it...

- idku

At first, I will just simply determine when the function is increasing and when decreasing, using the first derivative.

- idku

\(\tt f'(x)=3x^2+6x+2\)
This is the derivative, or the slope, of the function \(\tt f(x)\).
We know from elementary maths before calculuses, that:
\(\bullet\) When the slope is positive the function is increasing
\(\bullet\) When the slope is negative the function is decreasing

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- idku

So, we will set \(\tt f'(x)>0\) to find where the function is increasing, and set \(\tt f'(x)<0\) to find where the function is decreasing.

- idku

now, won't actually solve that... i need the concepts.

- idku

Ok, now, the critical numbers.

- idku

the critical numbers are the values of \(\tt f(x)\), are when:
1. \(\tt f'(x)=0\)
(will have to set the derivative =0 and solve for x)
2. \(\tt f'(x)\) is undefined (provided that \(\tt f(x)\) has a value at that point)
Polynomial is always continuous, and even without knowing this fact, I can tell that no restrictions in \(\tt f(x)\) or \(\tt f'(x)\) exist.

- idku

Then
\(\tt f'(b)=greatest~output~of~B\)
\(\tt f'(a)=smallest~output~of~A\)
when i check critical numbers, that would mean that I have
absolute maximum of B at x=b
absolute minimum of A at x=a

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