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Should I make a function up?
now will do a lot of things to it...
At first, I will just simply determine when the function is increasing and when decreasing, using the first derivative.
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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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.
now, won't actually solve that... i need the concepts.
Ok, now, the critical numbers.
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.
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